android-9.0.0_r3/s

# Copyright 2017 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
#     http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""This API defines FeatureColumn abstraction.

FeatureColumns provide a high level abstraction for ingesting and representing
features. FeatureColumns are also the primary way of encoding features for
canned ${tf.estimator.Estimator}s.

When using FeatureColumns with `Estimators`, the type of feature column you
should choose depends on (1) the feature type and (2) the model type.

1. Feature type:

  * Continuous features can be represented by `numeric_column`.
  * Categorical features can be represented by any `categorical_column_with_*`
  column:
    - `categorical_column_with_vocabulary_list`
    - `categorical_column_with_vocabulary_file`
    - `categorical_column_with_hash_bucket`
    - `categorical_column_with_identity`
    - `weighted_categorical_column`

2. Model type:

  * Deep neural network models (`DNNClassifier`, `DNNRegressor`).

    Continuous features can be directly fed into deep neural network models.

      age_column = numeric_column("age")

    To feed sparse features into DNN models, wrap the column with
    `embedding_column` or `indicator_column`. `indicator_column` is recommended
    for features with only a few possible values. For features with many
    possible values, to reduce the size of your model, `embedding_column` is
    recommended.

      embedded_dept_column = embedding_column(
          categorical_column_with_vocabulary_list(
              "department", ["math", "philosphy", ...]), dimension=10)

  * Wide (aka linear) models (`LinearClassifier`, `LinearRegressor`).

    Sparse features can be fed directly into linear models. They behave like an
    indicator column but with an efficient implementation.

      dept_column = categorical_column_with_vocabulary_list("department",
          ["math", "philosophy", "english"])

    It is recommended that continuous features be bucketized before being
    fed into linear models.

      bucketized_age_column = bucketized_column(
          source_column=age_column,
          boundaries=[18, 25, 30, 35, 40, 45, 50, 55, 60, 65])

    Sparse features can be crossed (also known as conjuncted or combined) in
    order to form non-linearities, and then fed into linear models.

      cross_dept_age_column = crossed_column(
          columns=["department", bucketized_age_column],
          hash_bucket_size=1000)

Example of building canned `Estimator`s using FeatureColumns:

  ```python
  # Define features and transformations
  deep_feature_columns = [age_column, embedded_dept_column]
  wide_feature_columns = [dept_column, bucketized_age_column,
      cross_dept_age_column]

  # Build deep model
  estimator = DNNClassifier(
      feature_columns=deep_feature_columns,
      hidden_units=[500, 250, 50])
  estimator.train(...)

  # Or build a wide model
  estimator = LinearClassifier(
      feature_columns=wide_feature_columns)
  estimator.train(...)

  # Or build a wide and deep model!
  estimator = DNNLinearCombinedClassifier(
      linear_feature_columns=wide_feature_columns,
      dnn_feature_columns=deep_feature_columns,
      dnn_hidden_units=[500, 250, 50])
  estimator.train(...)
  ```


FeatureColumns can also be transformed into a generic input layer for
custom models using `input_layer`.

Example of building model using FeatureColumns, this can be used in a
`model_fn` which is given to the {tf.estimator.Estimator}:

  ```python
  # Building model via layers

  deep_feature_columns = [age_column, embedded_dept_column]
  columns_to_tensor = parse_feature_columns_from_examples(
      serialized=my_data,
      feature_columns=deep_feature_columns)
  first_layer = input_layer(
      features=columns_to_tensor,
      feature_columns=deep_feature_columns)
  second_layer = fully_connected(first_layer, ...)
  ```

NOTE: Functions prefixed with "_" indicate experimental or private parts of
the API subject to change, and should not be relied upon!
"""

from __future__ import absolute_import
from __future__ import division
from __future__ import print_function

import abc
import collections
import math

import numpy as np
import six


from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.framework import sparse_tensor as sparse_tensor_lib
from tensorflow.python.framework import tensor_shape
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import check_ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import embedding_ops
from tensorflow.python.ops import init_ops
from tensorflow.python.ops import lookup_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import nn_ops
from tensorflow.python.ops import parsing_ops
from tensorflow.python.ops import sparse_ops
from tensorflow.python.ops import string_ops
from tensorflow.python.ops import template
from tensorflow.python.ops import variable_scope
from tensorflow.python.ops import variables
from tensorflow.python.platform import gfile
from tensorflow.python.platform import tf_logging as logging
from tensorflow.python.training import checkpoint_utils
from tensorflow.python.util import nest
from tensorflow.python.util.tf_export import tf_export
from tensorflow.python.util.tf_export import tf_export


def _internal_input_layer(features,
                          feature_columns,
                          weight_collections=None,
                          trainable=True,
                          cols_to_vars=None,
                          scope=None):
  """See input_layer. `scope` is a name or variable scope to use."""

  feature_columns = _clean_feature_columns(feature_columns)
  for column in feature_columns:
    if not isinstance(column, _DenseColumn):
      raise ValueError(
          'Items of feature_columns must be a _DenseColumn. '
          'You can wrap a categorical column with an '
          'embedding_column or indicator_column. Given: {}'.format(column))
  weight_collections = list(weight_collections or [])
  if ops.GraphKeys.GLOBAL_VARIABLES not in weight_collections:
    weight_collections.append(ops.GraphKeys.GLOBAL_VARIABLES)
  if ops.GraphKeys.MODEL_VARIABLES not in weight_collections:
    weight_collections.append(ops.GraphKeys.MODEL_VARIABLES)

  # a non-None `scope` can allow for variable reuse, when, e.g., this function
  # is wrapped by a `make_template`.
  with variable_scope.variable_scope(
      scope, default_name='input_layer', values=features.values()):
    builder = _LazyBuilder(features)
    output_tensors = []
    ordered_columns = []
    for column in sorted(feature_columns, key=lambda x: x.name):
      ordered_columns.append(column)
      with variable_scope.variable_scope(
          None, default_name=column._var_scope_name):  # pylint: disable=protected-access
        tensor = column._get_dense_tensor(  # pylint: disable=protected-access
            builder,
            weight_collections=weight_collections,
            trainable=trainable)
        num_elements = column._variable_shape.num_elements()  # pylint: disable=protected-access
        batch_size = array_ops.shape(tensor)[0]
        output_tensors.append(
            array_ops.reshape(tensor, shape=(batch_size, num_elements)))
        if cols_to_vars is not None:
          # Retrieve any variables created (some _DenseColumn's don't create
          # variables, in which case an empty list is returned).
          cols_to_vars[column] = ops.get_collection(
              ops.GraphKeys.GLOBAL_VARIABLES,
              scope=variable_scope.get_variable_scope().name)
    _verify_static_batch_size_equality(output_tensors, ordered_columns)
    return array_ops.concat(output_tensors, 1)


@tf_export('feature_column.input_layer')
def input_layer(features,
                feature_columns,
                weight_collections=None,
                trainable=True,
                cols_to_vars=None):
  """Returns a dense `Tensor` as input layer based on given `feature_columns`.

  Generally a single example in training data is described with FeatureColumns.
  At the first layer of the model, this column oriented data should be converted
  to a single `Tensor`.

  Example:

  ```python
  price = numeric_column('price')
  keywords_embedded = embedding_column(
      categorical_column_with_hash_bucket("keywords", 10K), dimensions=16)
  columns = [price, keywords_embedded, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)
  for units in [128, 64, 32]:
    dense_tensor = tf.layers.dense(dense_tensor, units, tf.nn.relu)
  prediction = tf.layers.dense(dense_tensor, 1)
  ```

  Args:
    features: A mapping from key to tensors. `_FeatureColumn`s look up via these
      keys. For example `numeric_column('price')` will look at 'price' key in
      this dict. Values can be a `SparseTensor` or a `Tensor` depends on
      corresponding `_FeatureColumn`.
    feature_columns: An iterable containing the FeatureColumns to use as inputs
      to your model. All items should be instances of classes derived from
      `_DenseColumn` such as `numeric_column`, `embedding_column`,
      `bucketized_column`, `indicator_column`. If you have categorical features,
      you can wrap them with an `embedding_column` or `indicator_column`.
    weight_collections: A list of collection names to which the Variable will be
      added. Note that variables will also be added to collections
      `tf.GraphKeys.GLOBAL_VARIABLES` and `ops.GraphKeys.MODEL_VARIABLES`.
    trainable: If `True` also add the variable to the graph collection
      `GraphKeys.TRAINABLE_VARIABLES` (see `tf.Variable`).
    cols_to_vars: If not `None`, must be a dictionary that will be filled with a
      mapping from `_FeatureColumn` to list of `Variable`s.  For example, after
      the call, we might have cols_to_vars =
      {_EmbeddingColumn(
        categorical_column=_HashedCategoricalColumn(
          key='sparse_feature', hash_bucket_size=5, dtype=tf.string),
        dimension=10): [<tf.Variable 'some_variable:0' shape=(5, 10),
                        <tf.Variable 'some_variable:1' shape=(5, 10)]}
      If a column creates no variables, its value will be an empty list.

  Returns:
    A `Tensor` which represents input layer of a model. Its shape
    is (batch_size, first_layer_dimension) and its dtype is `float32`.
    first_layer_dimension is determined based on given `feature_columns`.

  Raises:
    ValueError: if an item in `feature_columns` is not a `_DenseColumn`.
  """
  return _internal_input_layer(features, feature_columns, weight_collections,
                               trainable, cols_to_vars)


# TODO(akshayka): InputLayer should be a subclass of Layer, and it
# should implement the logic in input_layer using Layer's build-and-call
# paradigm; input_layer should create an instance of InputLayer and
# return the result of inovking its apply method, just as functional layers do.
class InputLayer(object):
  """An object-oriented version of `input_layer` that reuses variables."""

  def __init__(self,
               feature_columns,
               weight_collections=None,
               trainable=True,
               cols_to_vars=None):
    """See `input_layer`."""

    self._feature_columns = feature_columns
    self._weight_collections = weight_collections
    self._trainable = trainable
    self._cols_to_vars = cols_to_vars
    self._input_layer_template = template.make_template(
        'feature_column_input_layer',
        _internal_input_layer,
        create_scope_now_=True)
    self._scope = self._input_layer_template.variable_scope

  def __call__(self, features):
    return self._input_layer_template(
        features=features,
        feature_columns=self._feature_columns,
        weight_collections=self._weight_collections,
        trainable=self._trainable,
        cols_to_vars=None,
        scope=self._scope)

  @property
  def non_trainable_variables(self):
    return self._input_layer_template.non_trainable_variables

  @property
  def non_trainable_weights(self):
    return self._input_layer_template.non_trainable_weights

  @property
  def trainable_variables(self):
    return self._input_layer_template.trainable_variables

  @property
  def trainable_weights(self):
    return self._input_layer_template.trainable_weights

  @property
  def variables(self):
    return self._input_layer_template.variables

  @property
  def weights(self):
    return self._input_layer_template.weights


@tf_export('feature_column.linear_model')
def linear_model(features,
                 feature_columns,
                 units=1,
                 sparse_combiner='sum',
                 weight_collections=None,
                 trainable=True,
                 cols_to_vars=None):
  """Returns a linear prediction `Tensor` based on given `feature_columns`.

  This function generates a weighted sum based on output dimension `units`.
  Weighted sum refers to logits in classification problems. It refers to the
  prediction itself for linear regression problems.

  Note on supported columns: `linear_model` treats categorical columns as
  `indicator_column`s while `input_layer` explicitly requires wrapping each
  of them with an `embedding_column` or an `indicator_column`.

  Example:

  ```python
  price = numeric_column('price')
  price_buckets = bucketized_column(price, boundaries=[0., 10., 100., 1000.])
  keywords = categorical_column_with_hash_bucket("keywords", 10K)
  keywords_price = crossed_column('keywords', price_buckets, ...)
  columns = [price_buckets, keywords, keywords_price ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  prediction = linear_model(features, columns)
  ```

  Args:
    features: A mapping from key to tensors. `_FeatureColumn`s look up via these
      keys. For example `numeric_column('price')` will look at 'price' key in
      this dict. Values are `Tensor` or `SparseTensor` depending on
      corresponding `_FeatureColumn`.
    feature_columns: An iterable containing the FeatureColumns to use as inputs
      to your model. All items should be instances of classes derived from
      `_FeatureColumn`s.
    units: An integer, dimensionality of the output space. Default value is 1.
    sparse_combiner: A string specifying how to reduce if a sparse column is
      multivalent. Currently "mean", "sqrtn" and "sum" are supported, with "sum"
      the default. "sqrtn" often achieves good accuracy, in particular with
      bag-of-words columns. It combines each sparse columns independently.
        * "sum": do not normalize features in the column
        * "mean": do l1 normalization on features in the column
        * "sqrtn": do l2 normalization on features in the column
    weight_collections: A list of collection names to which the Variable will be
      added. Note that, variables will also be added to collections
      `tf.GraphKeys.GLOBAL_VARIABLES` and `ops.GraphKeys.MODEL_VARIABLES`.
    trainable: If `True` also add the variable to the graph collection
      `GraphKeys.TRAINABLE_VARIABLES` (see `tf.Variable`).
    cols_to_vars: If not `None`, must be a dictionary that will be filled with a
      mapping from `_FeatureColumn` to associated list of `Variable`s.  For
      example, after the call, we might have cols_to_vars = {
        _NumericColumn(
          key='numeric_feature1', shape=(1,):
        [<tf.Variable 'linear_model/price2/weights:0' shape=(1, 1)>],
        'bias': [<tf.Variable 'linear_model/bias_weights:0' shape=(1,)>],
        _NumericColumn(
          key='numeric_feature2', shape=(2,)):
        [<tf.Variable 'linear_model/price1/weights:0' shape=(2, 1)>]}
      If a column creates no variables, its value will be an empty list. Note
      that cols_to_vars will also contain a string key 'bias' that maps to a
      list of Variables.

  Returns:
    A `Tensor` which represents predictions/logits of a linear model. Its shape
    is (batch_size, units) and its dtype is `float32`.

  Raises:
    ValueError: if an item in `feature_columns` is neither a `_DenseColumn`
      nor `_CategoricalColumn`.
  """
  feature_columns = _clean_feature_columns(feature_columns)
  for column in feature_columns:
    if not isinstance(column, (_DenseColumn, _CategoricalColumn)):
      raise ValueError('Items of feature_columns must be either a _DenseColumn '
                       'or _CategoricalColumn. Given: {}'.format(column))
  weight_collections = list(weight_collections or [])
  if ops.GraphKeys.GLOBAL_VARIABLES not in weight_collections:
    weight_collections.append(ops.GraphKeys.GLOBAL_VARIABLES)
  if ops.GraphKeys.MODEL_VARIABLES not in weight_collections:
    weight_collections.append(ops.GraphKeys.MODEL_VARIABLES)
  with variable_scope.variable_scope(
      None, default_name='linear_model', values=features.values()):
    weighted_sums = []
    ordered_columns = []
    builder = _LazyBuilder(features)
    for column in sorted(feature_columns, key=lambda x: x.name):
      with variable_scope.variable_scope(
          None, default_name=column._var_scope_name):  # pylint: disable=protected-access
        ordered_columns.append(column)
        weighted_sum = _create_weighted_sum(
            column=column,
            builder=builder,
            units=units,
            sparse_combiner=sparse_combiner,
            weight_collections=weight_collections,
            trainable=trainable)
        weighted_sums.append(weighted_sum)
        if cols_to_vars is not None:
          # Retrieve the variables created.
          cols_to_vars[column] = ops.get_collection(
              ops.GraphKeys.GLOBAL_VARIABLES,
              scope=variable_scope.get_variable_scope().name)
    _verify_static_batch_size_equality(weighted_sums, ordered_columns)
    predictions_no_bias = math_ops.add_n(
        weighted_sums, name='weighted_sum_no_bias')
    bias = variable_scope.get_variable(
        'bias_weights',
        shape=[units],
        initializer=init_ops.zeros_initializer(),
        trainable=trainable,
        collections=weight_collections)
    predictions = nn_ops.bias_add(
        predictions_no_bias, bias, name='weighted_sum')
    if cols_to_vars is not None:
      # Add the bias to cols_to_vars as well, converting the Variable or
      # PartitionedVariable to a list of Variable's.
      if isinstance(bias, variables.Variable):
        cols_to_vars['bias'] = [bias]
      else:  # Must be a PartitionedVariable.
        cols_to_vars['bias'] = list(bias)
    return predictions


def _transform_features(features, feature_columns):
  """Returns transformed features based on features columns passed in.

  Please note that most probably you would not need to use this function. Please
  check `input_layer` and `linear_model` to see whether they will
  satisfy your use case or not.

  Example:

  ```python
  # Define features and transformations
  crosses_a_x_b = crossed_column(
      columns=["sparse_feature_a", "sparse_feature_b"], hash_bucket_size=10000)
  price_buckets = bucketized_column(
      source_column=numeric_column("price"), boundaries=[...])

  columns = [crosses_a_x_b, price_buckets]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  transformed = transform_features(features=features, feature_columns=columns)

  assertCountEqual(columns, transformed.keys())
  ```

  Args:
    features: A mapping from key to tensors. `_FeatureColumn`s look up via these
      keys. For example `numeric_column('price')` will look at 'price' key in
      this dict. Values can be a `SparseTensor` or a `Tensor` depends on
      corresponding `_FeatureColumn`.
    feature_columns: An iterable containing all the `_FeatureColumn`s.

  Returns:
    A `dict` mapping `_FeatureColumn` to `Tensor` and `SparseTensor` values.
  """
  feature_columns = _clean_feature_columns(feature_columns)
  outputs = {}
  with ops.name_scope(
      None, default_name='transform_features', values=features.values()):
    builder = _LazyBuilder(features)
    for column in sorted(feature_columns, key=lambda x: x.name):
      with ops.name_scope(None, default_name=column.name):
        outputs[column] = builder.get(column)
  return outputs


@tf_export('feature_column.make_parse_example_spec')
def make_parse_example_spec(feature_columns):
  """Creates parsing spec dictionary from input feature_columns.

  The returned dictionary can be used as arg 'features' in `tf.parse_example`.

  Typical usage example:

  ```python
  # Define features and transformations
  feature_a = categorical_column_with_vocabulary_file(...)
  feature_b = numeric_column(...)
  feature_c_bucketized = bucketized_column(numeric_column("feature_c"), ...)
  feature_a_x_feature_c = crossed_column(
      columns=["feature_a", feature_c_bucketized], ...)

  feature_columns = set(
      [feature_b, feature_c_bucketized, feature_a_x_feature_c])
  features = tf.parse_example(
      serialized=serialized_examples,
      features=make_parse_example_spec(feature_columns))
  ```

  For the above example, make_parse_example_spec would return the dict:

  ```python
  {
      "feature_a": parsing_ops.VarLenFeature(tf.string),
      "feature_b": parsing_ops.FixedLenFeature([1], dtype=tf.float32),
      "feature_c": parsing_ops.FixedLenFeature([1], dtype=tf.float32)
  }
  ```

  Args:
    feature_columns: An iterable containing all feature columns. All items
      should be instances of classes derived from `_FeatureColumn`.

  Returns:
    A dict mapping each feature key to a `FixedLenFeature` or `VarLenFeature`
    value.

  Raises:
    ValueError: If any of the given `feature_columns` is not a `_FeatureColumn`
      instance.
  """
  result = {}
  for column in feature_columns:
    if not isinstance(column, _FeatureColumn):
      raise ValueError(
          'All feature_columns must be _FeatureColumn instances. '
          'Given: {}'.format(column))
    config = column._parse_example_spec  # pylint: disable=protected-access
    for key, value in six.iteritems(config):
      if key in result and value != result[key]:
        raise ValueError(
            'feature_columns contain different parse_spec for key '
            '{}. Given {} and {}'.format(key, value, result[key]))
    result.update(config)
  return result


@tf_export('feature_column.embedding_column')
def embedding_column(
    categorical_column, dimension, combiner='mean', initializer=None,
    ckpt_to_load_from=None, tensor_name_in_ckpt=None, max_norm=None,
    trainable=True):
  """`_DenseColumn` that converts from sparse, categorical input.

  Use this when your inputs are sparse, but you want to convert them to a dense
  representation (e.g., to feed to a DNN).

  Inputs must be a `_CategoricalColumn` created by any of the
  `categorical_column_*` function. Here is an example of using
  `embedding_column` with `DNNClassifier`:

  ```python
  video_id = categorical_column_with_identity(
      key='video_id', num_buckets=1000000, default_value=0)
  columns = [embedding_column(video_id, 9),...]

  estimator = tf.estimator.DNNClassifier(feature_columns=columns, ...)

  label_column = ...
  def input_fn():
    features = tf.parse_example(
        ..., features=make_parse_example_spec(columns + [label_column]))
    labels = features.pop(label_column.name)
    return features, labels

  estimator.train(input_fn=input_fn, steps=100)
  ```

  Here is an example using `embedding_column` with model_fn:

  ```python
  def model_fn(features, ...):
    video_id = categorical_column_with_identity(
        key='video_id', num_buckets=1000000, default_value=0)
    columns = [embedding_column(video_id, 9),...]
    dense_tensor = input_layer(features, columns)
    # Form DNN layers, calculate loss, and return EstimatorSpec.
    ...
  ```

  Args:
    categorical_column: A `_CategoricalColumn` created by a
      `categorical_column_with_*` function. This column produces the sparse IDs
      that are inputs to the embedding lookup.
    dimension: An integer specifying dimension of the embedding, must be > 0.
    combiner: A string specifying how to reduce if there are multiple entries
      in a single row. Currently 'mean', 'sqrtn' and 'sum' are supported, with
      'mean' the default. 'sqrtn' often achieves good accuracy, in particular
      with bag-of-words columns. Each of this can be thought as example level
      normalizations on the column. For more information, see
      `tf.embedding_lookup_sparse`.
    initializer: A variable initializer function to be used in embedding
      variable initialization. If not specified, defaults to
      `tf.truncated_normal_initializer` with mean `0.0` and standard deviation
      `1/sqrt(dimension)`.
    ckpt_to_load_from: String representing checkpoint name/pattern from which to
      restore column weights. Required if `tensor_name_in_ckpt` is not `None`.
    tensor_name_in_ckpt: Name of the `Tensor` in `ckpt_to_load_from` from
      which to restore the column weights. Required if `ckpt_to_load_from` is
      not `None`.
    max_norm: If not `None`, embedding values are l2-normalized to this value.
    trainable: Whether or not the embedding is trainable. Default is True.

  Returns:
    `_DenseColumn` that converts from sparse input.

  Raises:
    ValueError: if `dimension` not > 0.
    ValueError: if exactly one of `ckpt_to_load_from` and `tensor_name_in_ckpt`
      is specified.
    ValueError: if `initializer` is specified and is not callable.
    RuntimeError: If eager execution is enabled.
  """
  if (dimension is None) or (dimension < 1):
    raise ValueError('Invalid dimension {}.'.format(dimension))
  if (ckpt_to_load_from is None) != (tensor_name_in_ckpt is None):
    raise ValueError('Must specify both `ckpt_to_load_from` and '
                     '`tensor_name_in_ckpt` or none of them.')

  if (initializer is not None) and (not callable(initializer)):
    raise ValueError('initializer must be callable if specified. '
                     'Embedding of column_name: {}'.format(
                         categorical_column.name))
  if initializer is None:
    initializer = init_ops.truncated_normal_initializer(
        mean=0.0, stddev=1 / math.sqrt(dimension))

  return _EmbeddingColumn(
      categorical_column=categorical_column,
      dimension=dimension,
      combiner=combiner,
      initializer=initializer,
      ckpt_to_load_from=ckpt_to_load_from,
      tensor_name_in_ckpt=tensor_name_in_ckpt,
      max_norm=max_norm,
      trainable=trainable)


@tf_export('feature_column.shared_embedding_columns')
def shared_embedding_columns(
    categorical_columns, dimension, combiner='mean', initializer=None,
    shared_embedding_collection_name=None, ckpt_to_load_from=None,
    tensor_name_in_ckpt=None, max_norm=None, trainable=True):
  """List of dense columns that convert from sparse, categorical input.

  This is similar to `embedding_column`, except that that it produces a list of
  embedding columns that share the same embedding weights.

  Use this when your inputs are sparse and of the same type (e.g. watched and
  impression video IDs that share the same vocabulary), and you want to convert
  them to a dense representation (e.g., to feed to a DNN).

  Inputs must be a list of categorical columns created by any of the
  `categorical_column_*` function. They must all be of the same type and have
  the same arguments except `key`. E.g. they can be
  categorical_column_with_vocabulary_file with the same vocabulary_file. Some or
  all columns could also be weighted_categorical_column.

  Here is an example embedding of two features for a DNNClassifier model:

  ```python
  watched_video_id = categorical_column_with_vocabulary_file(
      'watched_video_id', video_vocabulary_file, video_vocabulary_size)
  impression_video_id = categorical_column_with_vocabulary_file(
      'impression_video_id', video_vocabulary_file, video_vocabulary_size)
  columns = shared_embedding_columns(
      [watched_video_id, impression_video_id], dimension=10)

  estimator = tf.estimator.DNNClassifier(feature_columns=columns, ...)

  label_column = ...
  def input_fn():
    features = tf.parse_example(
        ..., features=make_parse_example_spec(columns + [label_column]))
    labels = features.pop(label_column.name)
    return features, labels

  estimator.train(input_fn=input_fn, steps=100)
  ```

  Here is an example using `shared_embedding_columns` with model_fn:

  ```python
  def model_fn(features, ...):
    watched_video_id = categorical_column_with_vocabulary_file(
        'watched_video_id', video_vocabulary_file, video_vocabulary_size)
    impression_video_id = categorical_column_with_vocabulary_file(
        'impression_video_id', video_vocabulary_file, video_vocabulary_size)
    columns = shared_embedding_columns(
        [watched_video_id, impression_video_id], dimension=10)
    dense_tensor = input_layer(features, columns)
    # Form DNN layers, calculate loss, and return EstimatorSpec.
    ...
  ```

  Args:
    categorical_columns: List of categorical columns created by a
      `categorical_column_with_*` function. These columns produce the sparse IDs
      that are inputs to the embedding lookup. All columns must be of the same
      type and have the same arguments except `key`. E.g. they can be
      categorical_column_with_vocabulary_file with the same vocabulary_file.
      Some or all columns could also be weighted_categorical_column.
    dimension: An integer specifying dimension of the embedding, must be > 0.
    combiner: A string specifying how to reduce if there are multiple entries
      in a single row. Currently 'mean', 'sqrtn' and 'sum' are supported, with
      'mean' the default. 'sqrtn' often achieves good accuracy, in particular
      with bag-of-words columns. Each of this can be thought as example level
      normalizations on the column. For more information, see
      `tf.embedding_lookup_sparse`.
    initializer: A variable initializer function to be used in embedding
      variable initialization. If not specified, defaults to
      `tf.truncated_normal_initializer` with mean `0.0` and standard deviation
      `1/sqrt(dimension)`.
    shared_embedding_collection_name: Optional name of the collection where
      shared embedding weights are added. If not given, a reasonable name will
      be chosen based on the names of `categorical_columns`. This is also used
      in `variable_scope` when creating shared embedding weights.
    ckpt_to_load_from: String representing checkpoint name/pattern from which to
      restore column weights. Required if `tensor_name_in_ckpt` is not `None`.
    tensor_name_in_ckpt: Name of the `Tensor` in `ckpt_to_load_from` from
      which to restore the column weights. Required if `ckpt_to_load_from` is
      not `None`.
    max_norm: If not `None`, embedding values are l2-normalized to this value.
    trainable: Whether or not the embedding is trainable. Default is True.

  Returns:
    A list of dense columns that converts from sparse input. The order of
    results follows the ordering of `categorical_columns`.

  Raises:
    ValueError: if `dimension` not > 0.
    ValueError: if any of the given `categorical_columns` is of different type
      or has different arguments than the others.
    ValueError: if exactly one of `ckpt_to_load_from` and `tensor_name_in_ckpt`
      is specified.
    ValueError: if `initializer` is specified and is not callable.
  """
  if (dimension is None) or (dimension < 1):
    raise ValueError('Invalid dimension {}.'.format(dimension))
  if (ckpt_to_load_from is None) != (tensor_name_in_ckpt is None):
    raise ValueError('Must specify both `ckpt_to_load_from` and '
                     '`tensor_name_in_ckpt` or none of them.')

  if (initializer is not None) and (not callable(initializer)):
    raise ValueError('initializer must be callable if specified.')
  if initializer is None:
    initializer = init_ops.truncated_normal_initializer(
        mean=0.0, stddev=1. / math.sqrt(dimension))

  # Sort the columns so the default collection name is deterministic even if the
  # user passes columns from an unsorted collection, such as dict.values().
  sorted_columns = sorted(categorical_columns, key=lambda x: x.name)

  c0 = sorted_columns[0]
  if not isinstance(c0, _CategoricalColumn):
    raise ValueError(
        'All categorical_columns must be subclasses of _CategoricalColumn. '
        'Given: {}, of type: {}'.format(c0, type(c0)))
  if isinstance(c0, _WeightedCategoricalColumn):
    c0 = c0.categorical_column
  for c in sorted_columns[1:]:
    if isinstance(c, _WeightedCategoricalColumn):
      c = c.categorical_column
    if not isinstance(c, type(c0)):
      raise ValueError(
          'To use shared_embedding_column, all categorical_columns must have '
          'the same type, or be weighted_categorical_column of the same type. '
          'Given column: {} of type: {} does not match given column: {} of '
          'type: {}'.format(c0, type(c0), c, type(c)))

  if not shared_embedding_collection_name:
    shared_embedding_collection_name = '_'.join(c.name for c in sorted_columns)
    shared_embedding_collection_name += '_shared_embedding'

  result = []
  for column in categorical_columns:
    result.append(_SharedEmbeddingColumn(
        categorical_column=column,
        dimension=dimension,
        combiner=combiner,
        initializer=initializer,
        shared_embedding_collection_name=shared_embedding_collection_name,
        ckpt_to_load_from=ckpt_to_load_from,
        tensor_name_in_ckpt=tensor_name_in_ckpt,
        max_norm=max_norm,
        trainable=trainable))
  return result


@tf_export('feature_column.numeric_column')
def numeric_column(key,
                   shape=(1,),
                   default_value=None,
                   dtype=dtypes.float32,
                   normalizer_fn=None):
  """Represents real valued or numerical features.

  Example:

  ```python
  price = numeric_column('price')
  columns = [price, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)

  # or
  bucketized_price = bucketized_column(price, boundaries=[...])
  columns = [bucketized_price, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)
  ```

  Args:
    key: A unique string identifying the input feature. It is used as the
      column name and the dictionary key for feature parsing configs, feature
      `Tensor` objects, and feature columns.
    shape: An iterable of integers specifies the shape of the `Tensor`. An
      integer can be given which means a single dimension `Tensor` with given
      width. The `Tensor` representing the column will have the shape of
      [batch_size] + `shape`.
    default_value: A single value compatible with `dtype` or an iterable of
      values compatible with `dtype` which the column takes on during
      `tf.Example` parsing if data is missing. A default value of `None` will
      cause `tf.parse_example` to fail if an example does not contain this
      column. If a single value is provided, the same value will be applied as
      the default value for every item. If an iterable of values is provided,
      the shape of the `default_value` should be equal to the given `shape`.
    dtype: defines the type of values. Default value is `tf.float32`. Must be a
      non-quantized, real integer or floating point type.
    normalizer_fn: If not `None`, a function that can be used to normalize the
      value of the tensor after `default_value` is applied for parsing.
      Normalizer function takes the input `Tensor` as its argument, and returns
      the output `Tensor`. (e.g. lambda x: (x - 3.0) / 4.2). Please note that
      even though the most common use case of this function is normalization, it
      can be used for any kind of Tensorflow transformations.

  Returns:
    A `_NumericColumn`.

  Raises:
    TypeError: if any dimension in shape is not an int
    ValueError: if any dimension in shape is not a positive integer
    TypeError: if `default_value` is an iterable but not compatible with `shape`
    TypeError: if `default_value` is not compatible with `dtype`.
    ValueError: if `dtype` is not convertible to `tf.float32`.
  """
  shape = _check_shape(shape, key)
  if not (dtype.is_integer or dtype.is_floating):
    raise ValueError('dtype must be convertible to float. '
                     'dtype: {}, key: {}'.format(dtype, key))
  default_value = _check_default_value(shape, default_value, dtype, key)

  if normalizer_fn is not None and not callable(normalizer_fn):
    raise TypeError(
        'normalizer_fn must be a callable. Given: {}'.format(normalizer_fn))

  return _NumericColumn(
      key,
      shape=shape,
      default_value=default_value,
      dtype=dtype,
      normalizer_fn=normalizer_fn)


@tf_export('feature_column.bucketized_column')
def bucketized_column(source_column, boundaries):
  """Represents discretized dense input.

  Buckets include the left boundary, and exclude the right boundary. Namely,
  `boundaries=[0., 1., 2.]` generates buckets `(-inf, 0.)`, `[0., 1.)`,
  `[1., 2.)`, and `[2., +inf)`.

  For example, if the inputs are

  ```python
  boundaries = [0, 10, 100]
  input tensor = [[-5, 10000]
                  [150,   10]
                  [5,    100]]
  ```

  then the output will be

  ```python
  output = [[0, 3]
            [3, 2]
            [1, 3]]
  ```

  Example:

  ```python
  price = numeric_column('price')
  bucketized_price = bucketized_column(price, boundaries=[...])
  columns = [bucketized_price, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)

  # or
  columns = [bucketized_price, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)
  ```

  `bucketized_column` can also be crossed with another categorical column using
  `crossed_column`:

  ```python
  price = numeric_column('price')
  # bucketized_column converts numerical feature to a categorical one.
  bucketized_price = bucketized_column(price, boundaries=[...])
  # 'keywords' is a string feature.
  price_x_keywords = crossed_column([bucketized_price, 'keywords'], 50K)
  columns = [price_x_keywords, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)
  ```

  Args:
    source_column: A one-dimensional dense column which is generated with
      `numeric_column`.
    boundaries: A sorted list or tuple of floats specifying the boundaries.

  Returns:
    A `_BucketizedColumn`.

  Raises:
    ValueError: If `source_column` is not a numeric column, or if it is not
      one-dimensional.
    ValueError: If `boundaries` is not a sorted list or tuple.
  """
  if not isinstance(source_column, _NumericColumn):
    raise ValueError(
        'source_column must be a column generated with numeric_column(). '
        'Given: {}'.format(source_column))
  if len(source_column.shape) > 1:
    raise ValueError(
        'source_column must be one-dimensional column. '
        'Given: {}'.format(source_column))
  if (not boundaries or
      not (isinstance(boundaries, list) or isinstance(boundaries, tuple))):
    raise ValueError('boundaries must be a sorted list.')
  for i in range(len(boundaries) - 1):
    if boundaries[i] >= boundaries[i + 1]:
      raise ValueError('boundaries must be a sorted list.')
  return _BucketizedColumn(source_column, tuple(boundaries))


def _assert_string_or_int(dtype, prefix):
  if (dtype != dtypes.string) and (not dtype.is_integer):
    raise ValueError(
        '{} dtype must be string or integer. dtype: {}.'.format(prefix, dtype))


@tf_export('feature_column.categorical_column_with_hash_bucket')
def categorical_column_with_hash_bucket(key,
                                        hash_bucket_size,
                                        dtype=dtypes.string):
  """Represents sparse feature where ids are set by hashing.

  Use this when your sparse features are in string or integer format, and you
  want to distribute your inputs into a finite number of buckets by hashing.
  output_id = Hash(input_feature_string) % bucket_size

  For input dictionary `features`, `features[key]` is either `Tensor` or
  `SparseTensor`. If `Tensor`, missing values can be represented by `-1` for int
  and `''` for string. Note that these values are independent of the
  `default_value` argument.

  Example:

  ```python
  keywords = categorical_column_with_hash_bucket("keywords", 10K)
  columns = [keywords, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)

  # or
  keywords_embedded = embedding_column(keywords, 16)
  columns = [keywords_embedded, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)
  ```

  Args:
    key: A unique string identifying the input feature. It is used as the
      column name and the dictionary key for feature parsing configs, feature
      `Tensor` objects, and feature columns.
    hash_bucket_size: An int > 1. The number of buckets.
    dtype: The type of features. Only string and integer types are supported.

  Returns:
    A `_HashedCategoricalColumn`.

  Raises:
    ValueError: `hash_bucket_size` is not greater than 1.
    ValueError: `dtype` is neither string nor integer.
  """
  if hash_bucket_size is None:
    raise ValueError('hash_bucket_size must be set. ' 'key: {}'.format(key))

  if hash_bucket_size < 1:
    raise ValueError('hash_bucket_size must be at least 1. '
                     'hash_bucket_size: {}, key: {}'.format(
                         hash_bucket_size, key))

  _assert_string_or_int(dtype, prefix='column_name: {}'.format(key))

  return _HashedCategoricalColumn(key, hash_bucket_size, dtype)


@tf_export('feature_column.categorical_column_with_vocabulary_file')
def categorical_column_with_vocabulary_file(key,
                                            vocabulary_file,
                                            vocabulary_size=None,
                                            num_oov_buckets=0,
                                            default_value=None,
                                            dtype=dtypes.string):
  """A `_CategoricalColumn` with a vocabulary file.

  Use this when your inputs are in string or integer format, and you have a
  vocabulary file that maps each value to an integer ID. By default,
  out-of-vocabulary values are ignored. Use either (but not both) of
  `num_oov_buckets` and `default_value` to specify how to include
  out-of-vocabulary values.

  For input dictionary `features`, `features[key]` is either `Tensor` or
  `SparseTensor`. If `Tensor`, missing values can be represented by `-1` for int
  and `''` for string. Note that these values are independent of the
  `default_value` argument.

  Example with `num_oov_buckets`:
  File '/us/states.txt' contains 50 lines, each with a 2-character U.S. state
  abbreviation. All inputs with values in that file are assigned an ID 0-49,
  corresponding to its line number. All other values are hashed and assigned an
  ID 50-54.

  ```python
  states = categorical_column_with_vocabulary_file(
      key='states', vocabulary_file='/us/states.txt', vocabulary_size=50,
      num_oov_buckets=5)
  columns = [states, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)
  ```

  Example with `default_value`:
  File '/us/states.txt' contains 51 lines - the first line is 'XX', and the
  other 50 each have a 2-character U.S. state abbreviation. Both a literal 'XX'
  in input, and other values missing from the file, will be assigned ID 0. All
  others are assigned the corresponding line number 1-50.

  ```python
  states = categorical_column_with_vocabulary_file(
      key='states', vocabulary_file='/us/states.txt', vocabulary_size=51,
      default_value=0)
  columns = [states, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction, _, _ = linear_model(features, columns)
  ```

  And to make an embedding with either:

  ```python
  columns = [embedding_column(states, 3),...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)
  ```

  Args:
    key: A unique string identifying the input feature. It is used as the
      column name and the dictionary key for feature parsing configs, feature
      `Tensor` objects, and feature columns.
    vocabulary_file: The vocabulary file name.
    vocabulary_size: Number of the elements in the vocabulary. This must be no
      greater than length of `vocabulary_file`, if less than length, later
      values are ignored. If None, it is set to the length of `vocabulary_file`.
    num_oov_buckets: Non-negative integer, the number of out-of-vocabulary
      buckets. All out-of-vocabulary inputs will be assigned IDs in the range
      `[vocabulary_size, vocabulary_size+num_oov_buckets)` based on a hash of
      the input value. A positive `num_oov_buckets` can not be specified with
      `default_value`.
    default_value: The integer ID value to return for out-of-vocabulary feature
      values, defaults to `-1`. This can not be specified with a positive
      `num_oov_buckets`.
    dtype: The type of features. Only string and integer types are supported.

  Returns:
    A `_CategoricalColumn` with a vocabulary file.

  Raises:
    ValueError: `vocabulary_file` is missing or cannot be opened.
    ValueError: `vocabulary_size` is missing or < 1.
    ValueError: `num_oov_buckets` is a negative integer.
    ValueError: `num_oov_buckets` and `default_value` are both specified.
    ValueError: `dtype` is neither string nor integer.
  """
  if not vocabulary_file:
    raise ValueError('Missing vocabulary_file in {}.'.format(key))

  if vocabulary_size is None:
    if not gfile.Exists(vocabulary_file):
      raise ValueError('vocabulary_file in {} does not exist.'.format(key))

    with gfile.GFile(vocabulary_file) as f:
      vocabulary_size = sum(1 for _ in f)
    logging.info(
        'vocabulary_size = %d in %s is inferred from the number of elements '
        'in the vocabulary_file %s.', vocabulary_size, key, vocabulary_file)

  # `vocabulary_size` isn't required for lookup, but it is for `_num_buckets`.
  if vocabulary_size < 1:
    raise ValueError('Invalid vocabulary_size in {}.'.format(key))
  if num_oov_buckets:
    if default_value is not None:
      raise ValueError(
          'Can\'t specify both num_oov_buckets and default_value in {}.'.format(
              key))
    if num_oov_buckets < 0:
      raise ValueError('Invalid num_oov_buckets {} in {}.'.format(
          num_oov_buckets, key))
  _assert_string_or_int(dtype, prefix='column_name: {}'.format(key))
  return _VocabularyFileCategoricalColumn(
      key=key,
      vocabulary_file=vocabulary_file,
      vocabulary_size=vocabulary_size,
      num_oov_buckets=0 if num_oov_buckets is None else num_oov_buckets,
      default_value=-1 if default_value is None else default_value,
      dtype=dtype)


@tf_export('feature_column.categorical_column_with_vocabulary_list')
def categorical_column_with_vocabulary_list(
    key, vocabulary_list, dtype=None, default_value=-1, num_oov_buckets=0):
  """A `_CategoricalColumn` with in-memory vocabulary.

  Use this when your inputs are in string or integer format, and you have an
  in-memory vocabulary mapping each value to an integer ID. By default,
  out-of-vocabulary values are ignored. Use either (but not both) of
  `num_oov_buckets` and `default_value` to specify how to include
  out-of-vocabulary values.

  For input dictionary `features`, `features[key]` is either `Tensor` or
  `SparseTensor`. If `Tensor`, missing values can be represented by `-1` for int
  and `''` for string. Note that these values are independent of the
  `default_value` argument.

  Example with `num_oov_buckets`:
  In the following example, each input in `vocabulary_list` is assigned an ID
  0-3 corresponding to its index (e.g., input 'B' produces output 2). All other
  inputs are hashed and assigned an ID 4-5.

  ```python
  colors = categorical_column_with_vocabulary_list(
      key='colors', vocabulary_list=('R', 'G', 'B', 'Y'),
      num_oov_buckets=2)
  columns = [colors, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction, _, _ = linear_model(features, columns)
  ```

  Example with `default_value`:
  In the following example, each input in `vocabulary_list` is assigned an ID
  0-4 corresponding to its index (e.g., input 'B' produces output 3). All other
  inputs are assigned `default_value` 0.


  ```python
  colors = categorical_column_with_vocabulary_list(
      key='colors', vocabulary_list=('X', 'R', 'G', 'B', 'Y'), default_value=0)
  columns = [colors, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction, _, _ = linear_model(features, columns)
  ```

  And to make an embedding with either:

  ```python
  columns = [embedding_column(colors, 3),...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)
  ```

  Args:
    key: A unique string identifying the input feature. It is used as the
      column name and the dictionary key for feature parsing configs, feature
      `Tensor` objects, and feature columns.
    vocabulary_list: An ordered iterable defining the vocabulary. Each feature
      is mapped to the index of its value (if present) in `vocabulary_list`.
      Must be castable to `dtype`.
    dtype: The type of features. Only string and integer types are supported.
      If `None`, it will be inferred from `vocabulary_list`.
    default_value: The integer ID value to return for out-of-vocabulary feature
      values, defaults to `-1`. This can not be specified with a positive
      `num_oov_buckets`.
    num_oov_buckets: Non-negative integer, the number of out-of-vocabulary
      buckets. All out-of-vocabulary inputs will be assigned IDs in the range
      `[len(vocabulary_list), len(vocabulary_list)+num_oov_buckets)` based on a
      hash of the input value. A positive `num_oov_buckets` can not be specified
      with `default_value`.

  Returns:
    A `_CategoricalColumn` with in-memory vocabulary.

  Raises:
    ValueError: if `vocabulary_list` is empty, or contains duplicate keys.
    ValueError: `num_oov_buckets` is a negative integer.
    ValueError: `num_oov_buckets` and `default_value` are both specified.
    ValueError: if `dtype` is not integer or string.
  """
  if (vocabulary_list is None) or (len(vocabulary_list) < 1):
    raise ValueError(
        'vocabulary_list {} must be non-empty, column_name: {}'.format(
            vocabulary_list, key))
  if len(set(vocabulary_list)) != len(vocabulary_list):
    raise ValueError(
        'Duplicate keys in vocabulary_list {}, column_name: {}'.format(
            vocabulary_list, key))
  vocabulary_dtype = dtypes.as_dtype(np.array(vocabulary_list).dtype)
  if num_oov_buckets:
    if default_value != -1:
      raise ValueError(
          'Can\'t specify both num_oov_buckets and default_value in {}.'.format(
              key))
    if num_oov_buckets < 0:
      raise ValueError('Invalid num_oov_buckets {} in {}.'.format(
          num_oov_buckets, key))
  _assert_string_or_int(
      vocabulary_dtype, prefix='column_name: {} vocabulary'.format(key))
  if dtype is None:
    dtype = vocabulary_dtype
  elif dtype.is_integer != vocabulary_dtype.is_integer:
    raise ValueError(
        'dtype {} and vocabulary dtype {} do not match, column_name: {}'.format(
            dtype, vocabulary_dtype, key))
  _assert_string_or_int(dtype, prefix='column_name: {}'.format(key))

  return _VocabularyListCategoricalColumn(
      key=key, vocabulary_list=tuple(vocabulary_list), dtype=dtype,
      default_value=default_value, num_oov_buckets=num_oov_buckets)


@tf_export('feature_column.categorical_column_with_identity')
def categorical_column_with_identity(key, num_buckets, default_value=None):
  """A `_CategoricalColumn` that returns identity values.

  Use this when your inputs are integers in the range `[0, num_buckets)`, and
  you want to use the input value itself as the categorical ID. Values outside
  this range will result in `default_value` if specified, otherwise it will
  fail.

  Typically, this is used for contiguous ranges of integer indexes, but
  it doesn't have to be. This might be inefficient, however, if many of IDs
  are unused. Consider `categorical_column_with_hash_bucket` in that case.

  For input dictionary `features`, `features[key]` is either `Tensor` or
  `SparseTensor`. If `Tensor`, missing values can be represented by `-1` for int
  and `''` for string. Note that these values are independent of the
  `default_value` argument.

  In the following examples, each input in the range `[0, 1000000)` is assigned
  the same value. All other inputs are assigned `default_value` 0. Note that a
  literal 0 in inputs will result in the same default ID.

  Linear model:

  ```python
  video_id = categorical_column_with_identity(
      key='video_id', num_buckets=1000000, default_value=0)
  columns = [video_id, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction, _, _ = linear_model(features, columns)
  ```

  Embedding for a DNN model:

  ```python
  columns = [embedding_column(video_id, 9),...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)
  ```

  Args:
    key: A unique string identifying the input feature. It is used as the
      column name and the dictionary key for feature parsing configs, feature
      `Tensor` objects, and feature columns.
    num_buckets: Range of inputs and outputs is `[0, num_buckets)`.
    default_value: If `None`, this column's graph operations will fail for
      out-of-range inputs. Otherwise, this value must be in the range
      `[0, num_buckets)`, and will replace inputs in that range.

  Returns:
    A `_CategoricalColumn` that returns identity values.

  Raises:
    ValueError: if `num_buckets` is less than one.
    ValueError: if `default_value` is not in range `[0, num_buckets)`.
  """
  if num_buckets < 1:
    raise ValueError(
        'num_buckets {} < 1, column_name {}'.format(num_buckets, key))
  if (default_value is not None) and (
      (default_value < 0) or (default_value >= num_buckets)):
    raise ValueError(
        'default_value {} not in range [0, {}), column_name {}'.format(
            default_value, num_buckets, key))
  return _IdentityCategoricalColumn(
      key=key, num_buckets=num_buckets, default_value=default_value)


@tf_export('feature_column.indicator_column')
def indicator_column(categorical_column):
  """Represents multi-hot representation of given categorical column.

  Used to wrap any `categorical_column_*` (e.g., to feed to DNN). Use
  `embedding_column` if the inputs are sparse.

  ```python
  name = indicator_column(categorical_column_with_vocabulary_list(
      'name', ['bob', 'george', 'wanda'])
  columns = [name, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  dense_tensor = input_layer(features, columns)

  dense_tensor == [[1, 0, 0]]  # If "name" bytes_list is ["bob"]
  dense_tensor == [[1, 0, 1]]  # If "name" bytes_list is ["bob", "wanda"]
  dense_tensor == [[2, 0, 0]]  # If "name" bytes_list is ["bob", "bob"]
  ```

  Args:
    categorical_column: A `_CategoricalColumn` which is created by
      `categorical_column_with_*` or `crossed_column` functions.

  Returns:
    An `_IndicatorColumn`.
  """
  return _IndicatorColumn(categorical_column)


@tf_export('feature_column.weighted_categorical_column')
def weighted_categorical_column(
    categorical_column, weight_feature_key, dtype=dtypes.float32):
  """Applies weight values to a `_CategoricalColumn`.

  Use this when each of your sparse inputs has both an ID and a value. For
  example, if you're representing text documents as a collection of word
  frequencies, you can provide 2 parallel sparse input features ('terms' and
  'frequencies' below).

  Example:

  Input `tf.Example` objects:

  ```proto
  [
    features {
      feature {
        key: "terms"
        value {bytes_list {value: "very" value: "model"}}
      }
      feature {
        key: "frequencies"
        value {float_list {value: 0.3 value: 0.1}}
      }
    },
    features {
      feature {
        key: "terms"
        value {bytes_list {value: "when" value: "course" value: "human"}}
      }
      feature {
        key: "frequencies"
        value {float_list {value: 0.4 value: 0.1 value: 0.2}}
      }
    }
  ]
  ```

  ```python
  categorical_column = categorical_column_with_hash_bucket(
      column_name='terms', hash_bucket_size=1000)
  weighted_column = weighted_categorical_column(
      categorical_column=categorical_column, weight_feature_key='frequencies')
  columns = [weighted_column, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction, _, _ = linear_model(features, columns)
  ```

  This assumes the input dictionary contains a `SparseTensor` for key
  'terms', and a `SparseTensor` for key 'frequencies'. These 2 tensors must have
  the same indices and dense shape.

  Args:
    categorical_column: A `_CategoricalColumn` created by
      `categorical_column_with_*` functions.
    weight_feature_key: String key for weight values.
    dtype: Type of weights, such as `tf.float32`. Only float and integer weights
      are supported.

  Returns:
    A `_CategoricalColumn` composed of two sparse features: one represents id,
    the other represents weight (value) of the id feature in that example.

  Raises:
    ValueError: if `dtype` is not convertible to float.
  """
  if (dtype is None) or not (dtype.is_integer or dtype.is_floating):
    raise ValueError('dtype {} is not convertible to float.'.format(dtype))
  return _WeightedCategoricalColumn(
      categorical_column=categorical_column,
      weight_feature_key=weight_feature_key,
      dtype=dtype)


@tf_export('feature_column.crossed_column')
def crossed_column(keys, hash_bucket_size, hash_key=None):
  """Returns a column for performing crosses of categorical features.

  Crossed features will be hashed according to `hash_bucket_size`. Conceptually,
  the transformation can be thought of as:
    Hash(cartesian product of features) % `hash_bucket_size`

  For example, if the input features are:

  * SparseTensor referred by first key:

    ```python
    shape = [2, 2]
    {
        [0, 0]: "a"
        [1, 0]: "b"
        [1, 1]: "c"
    }
    ```

  * SparseTensor referred by second key:

    ```python
    shape = [2, 1]
    {
        [0, 0]: "d"
        [1, 0]: "e"
    }
    ```

  then crossed feature will look like:

  ```python
   shape = [2, 2]
  {
      [0, 0]: Hash64("d", Hash64("a")) % hash_bucket_size
      [1, 0]: Hash64("e", Hash64("b")) % hash_bucket_size
      [1, 1]: Hash64("e", Hash64("c")) % hash_bucket_size
  }
  ```

  Here is an example to create a linear model with crosses of string features:

  ```python
  keywords_x_doc_terms = crossed_column(['keywords', 'doc_terms'], 50K)
  columns = [keywords_x_doc_terms, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)
  ```

  You could also use vocabulary lookup before crossing:

  ```python
  keywords = categorical_column_with_vocabulary_file(
      'keywords', '/path/to/vocabulary/file', vocabulary_size=1K)
  keywords_x_doc_terms = crossed_column([keywords, 'doc_terms'], 50K)
  columns = [keywords_x_doc_terms, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)
  ```

  If an input feature is of numeric type, you can use
  `categorical_column_with_identity`, or `bucketized_column`, as in the example:

  ```python
  # vertical_id is an integer categorical feature.
  vertical_id = categorical_column_with_identity('vertical_id', 10K)
  price = numeric_column('price')
  # bucketized_column converts numerical feature to a categorical one.
  bucketized_price = bucketized_column(price, boundaries=[...])
  vertical_id_x_price = crossed_column([vertical_id, bucketized_price], 50K)
  columns = [vertical_id_x_price, ...]
  features = tf.parse_example(..., features=make_parse_example_spec(columns))
  linear_prediction = linear_model(features, columns)
  ```

  To use crossed column in DNN model, you need to add it in an embedding column
  as in this example:

  ```python
  vertical_id_x_price = crossed_column([vertical_id, bucketized_price], 50K)
  vertical_id_x_price_embedded = embedding_column(vertical_id_x_price, 10)
  dense_tensor = input_layer(features, [vertical_id_x_price_embedded, ...])
  ```

  Args:
    keys: An iterable identifying the features to be crossed. Each element can
      be either:
      * string: Will use the corresponding feature which must be of string type.
      * `_CategoricalColumn`: Will use the transformed tensor produced by this
        column. Does not support hashed categorical column.
    hash_bucket_size: An int > 1. The number of buckets.
    hash_key: Specify the hash_key that will be used by the `FingerprintCat64`
      function to combine the crosses fingerprints on SparseCrossOp (optional).

  Returns:
    A `_CrossedColumn`.

  Raises:
    ValueError: If `len(keys) < 2`.
    ValueError: If any of the keys is neither a string nor `_CategoricalColumn`.
    ValueError: If any of the keys is `_HashedCategoricalColumn`.
    ValueError: If `hash_bucket_size < 1`.
  """
  if not hash_bucket_size or hash_bucket_size < 1:
    raise ValueError('hash_bucket_size must be > 1. '
                     'hash_bucket_size: {}'.format(hash_bucket_size))
  if not keys or len(keys) < 2:
    raise ValueError(
        'keys must be a list with length > 1. Given: {}'.format(keys))
  for key in keys:
    if (not isinstance(key, six.string_types) and
        not isinstance(key, _CategoricalColumn)):
      raise ValueError(
          'Unsupported key type. All keys must be either string, or '
          'categorical column except _HashedCategoricalColumn. '
          'Given: {}'.format(key))
    if isinstance(key, _HashedCategoricalColumn):
      raise ValueError(
          'categorical_column_with_hash_bucket is not supported for crossing. '
          'Hashing before crossing will increase probability of collision. '
          'Instead, use the feature name as a string. Given: {}'.format(key))
  return _CrossedColumn(
      keys=tuple(keys), hash_bucket_size=hash_bucket_size,
      hash_key=hash_key)


class _FeatureColumn(object):
  """Represents a feature column abstraction.

  WARNING: Do not subclass this layer unless you know what you are doing:
  the API is subject to future changes.

  To distinguish the concept of a feature family and a specific binary feature
  within a family, we refer to a feature family like "country" as a feature
  column. Following is an example feature in a `tf.Example` format:
    {key: "country",  value: [ "US" ]}
  In this example the value of feature is "US" and "country" refers to the
  column of the feature.

  This class is an abstract class. User should not create instances of this.
  """
  __metaclass__ = abc.ABCMeta

  @abc.abstractproperty
  def name(self):
    """Returns string. Used for naming and for name_scope."""
    pass

  @property
  def _var_scope_name(self):
    """Returns string. Used for variable_scope. Defaults to self.name."""
    return self.name

  @abc.abstractmethod
  def _transform_feature(self, inputs):
    """Returns intermediate representation (usually a `Tensor`).

    Uses `inputs` to create an intermediate representation (usually a `Tensor`)
    that other feature columns can use.

    Example usage of `inputs`:
    Let's say a Feature column depends on raw feature ('raw') and another
    `_FeatureColumn` (input_fc). To access corresponding `Tensor`s, inputs will
    be used as follows:

    ```python
    raw_tensor = inputs.get('raw')
    fc_tensor = inputs.get(input_fc)
    ```

    Args:
      inputs: A `_LazyBuilder` object to access inputs.

    Returns:
      Transformed feature `Tensor`.
    """
    pass

  @abc.abstractproperty
  def _parse_example_spec(self):
    """Returns a `tf.Example` parsing spec as dict.

    It is used for get_parsing_spec for `tf.parse_example`. Returned spec is a
    dict from keys ('string') to `VarLenFeature`, `FixedLenFeature`, and other
    supported objects. Please check documentation of ${tf.parse_example} for all
    supported spec objects.

    Let's say a Feature column depends on raw feature ('raw') and another
    `_FeatureColumn` (input_fc). One possible implementation of
    _parse_example_spec is as follows:

    ```python
    spec = {'raw': tf.FixedLenFeature(...)}
    spec.update(input_fc._parse_example_spec)
    return spec
    ```
    """
    pass


class _DenseColumn(_FeatureColumn):
  """Represents a column which can be represented as `Tensor`.

  WARNING: Do not subclass this layer unless you know what you are doing:
  the API is subject to future changes.

  Some examples of this type are: numeric_column, embedding_column,
  indicator_column.
  """

  __metaclass__ = abc.ABCMeta

  @abc.abstractproperty
  def _variable_shape(self):
    """`TensorShape` of `_get_dense_tensor`, without batch dimension."""
    pass

  @abc.abstractmethod
  def _get_dense_tensor(self, inputs, weight_collections=None, trainable=None):
    """Returns a `Tensor`.

    The output of this function will be used by model-builder-functions. For
    example the pseudo code of `input_layer` will be like:

    ```python
    def input_layer(features, feature_columns, ...):
      outputs = [fc._get_dense_tensor(...) for fc in feature_columns]
      return tf.concat(outputs)
    ```

    Args:
      inputs: A `_LazyBuilder` object to access inputs.
      weight_collections: List of graph collections to which Variables (if any
        will be created) are added.
      trainable: If `True` also add variables to the graph collection
        `GraphKeys.TRAINABLE_VARIABLES` (see ${tf.Variable}).

    Returns:
      `Tensor` of shape [batch_size] + `_variable_shape`.
    """
    pass


def _create_weighted_sum(
    column,
    builder,
    units,
    sparse_combiner,
    weight_collections,
    trainable):
  """Creates a weighted sum for a dense or sparse column for linear_model."""
  if isinstance(column, _CategoricalColumn):
    return _create_categorical_column_weighted_sum(
        column=column,
        builder=builder,
        units=units,
        sparse_combiner=sparse_combiner,
        weight_collections=weight_collections,
        trainable=trainable)
  else:
    return _create_dense_column_weighted_sum(
        column=column,
        builder=builder,
        units=units,
        weight_collections=weight_collections,
        trainable=trainable)


def _create_dense_column_weighted_sum(
    column, builder, units, weight_collections, trainable):
  """Create a weighted sum of a dense column for linear_model."""
  tensor = column._get_dense_tensor(  # pylint: disable=protected-access
      builder,
      weight_collections=weight_collections,
      trainable=trainable)
  num_elements = column._variable_shape.num_elements()  # pylint: disable=protected-access
  batch_size = array_ops.shape(tensor)[0]
  tensor = array_ops.reshape(tensor, shape=(batch_size, num_elements))
  weight = variable_scope.get_variable(
      name='weights',
      shape=[num_elements, units],
      initializer=init_ops.zeros_initializer(),
      trainable=trainable,
      collections=weight_collections)
  return math_ops.matmul(tensor, weight, name='weighted_sum')


class _CategoricalColumn(_FeatureColumn):
  """Represents a categorical feature.

  WARNING: Do not subclass this layer unless you know what you are doing:
  the API is subject to future changes.

  A categorical feature typically handled with a ${tf.SparseTensor} of IDs.
  """
  __metaclass__ = abc.ABCMeta

  IdWeightPair = collections.namedtuple(  # pylint: disable=invalid-name
      'IdWeightPair', ['id_tensor', 'weight_tensor'])

  @abc.abstractproperty
  def _num_buckets(self):
    """Returns number of buckets in this sparse feature."""
    pass

  @abc.abstractmethod
  def _get_sparse_tensors(self,
                          inputs,
                          weight_collections=None,
                          trainable=None):
    """Returns an IdWeightPair.

    `IdWeightPair` is a pair of `SparseTensor`s which represents ids and
    weights.

    `IdWeightPair.id_tensor` is typically a `batch_size` x `num_buckets`
    `SparseTensor` of `int64`. `IdWeightPair.weight_tensor` is either a
    `SparseTensor` of `float` or `None` to indicate all weights should be
    taken to be 1. If specified, `weight_tensor` must have exactly the same
    shape and indices as `sp_ids`. Expected `SparseTensor` is same as parsing
    output of a `VarLenFeature` which is a ragged matrix.

    Args:
      inputs: A `LazyBuilder` as a cache to get input tensors required to
        create `IdWeightPair`.
      weight_collections: List of graph collections to which variables (if any
        will be created) are added.
      trainable: If `True` also add variables to the graph collection
        `GraphKeys.TRAINABLE_VARIABLES` (see ${tf.get_variable}).
    """
    pass


def _create_categorical_column_weighted_sum(
    column, builder, units, sparse_combiner, weight_collections, trainable):
  """Create a weighted sum of a categorical column for linear_model."""
  sparse_tensors = column._get_sparse_tensors(  # pylint: disable=protected-access
      builder,
      weight_collections=weight_collections,
      trainable=trainable)
  id_tensor = sparse_ops.sparse_reshape(sparse_tensors.id_tensor, [
      array_ops.shape(sparse_tensors.id_tensor)[0], -1
  ])
  weight_tensor = sparse_tensors.weight_tensor
  if weight_tensor is not None:
    weight_tensor = sparse_ops.sparse_reshape(
        weight_tensor, [array_ops.shape(weight_tensor)[0], -1])

  weight = variable_scope.get_variable(
      name='weights',
      shape=(column._num_buckets, units),  # pylint: disable=protected-access
      initializer=init_ops.zeros_initializer(),
      trainable=trainable,
      collections=weight_collections)
  return _safe_embedding_lookup_sparse(
      weight,
      id_tensor,
      sparse_weights=weight_tensor,
      combiner=sparse_combiner,
      name='weighted_sum')


class _LazyBuilder(object):
  """Handles caching of transformations while building the model.

  `_FeatureColumn` specifies how to digest an input column to the network. Some
  feature columns require data transformations. This class caches those
  transformations.

  Some features may be used in more than one place. For example, one can use a
  bucketized feature by itself and a cross with it. In that case we
  should create only one bucketization op instead of creating ops for each
  feature column separately. To handle re-use of transformed columns,
  `_LazyBuilder` caches all previously transformed columns.

  Example:
  We're trying to use the following `_FeatureColumn`s:

  ```python
  bucketized_age = fc.bucketized_column(fc.numeric_column("age"), ...)
  keywords = fc.categorical_column_with_hash_buckets("keywords", ...)
  age_X_keywords = fc.crossed_column([bucketized_age, "keywords"])
  ... = linear_model(features,
                          [bucketized_age, keywords, age_X_keywords]
  ```

  If we transform each column independently, then we'll get duplication of
  bucketization (one for cross, one for bucketization itself).
  The `_LazyBuilder` eliminates this duplication.
  """

  def __init__(self, features):
    """Creates a `_LazyBuilder`.

    Args:
      features: A mapping from feature column to objects that are `Tensor` or
        `SparseTensor`, or can be converted to same via
        `sparse_tensor.convert_to_tensor_or_sparse_tensor`. A `string` key
        signifies a base feature (not-transformed). A `_FeatureColumn` key
        means that this `Tensor` is the output of an existing `_FeatureColumn`
        which can be reused.
    """
    self._features = features.copy()
    self._feature_tensors = {}

  def get(self, key):
    """Returns a `Tensor` for the given key.

    A `str` key is used to access a base feature (not-transformed). When a
    `_FeatureColumn` is passed, the transformed feature is returned if it
    already exists, otherwise the given `_FeatureColumn` is asked to provide its
    transformed output, which is then cached.

    Args:
      key: a `str` or a `_FeatureColumn`.

    Returns:
      The transformed `Tensor` corresponding to the `key`.

    Raises:
      ValueError: if key is not found or a transformed `Tensor` cannot be
        computed.
    """
    if key in self._feature_tensors:
      # FeatureColumn is already transformed or converted.
      return self._feature_tensors[key]

    if key in self._features:
      feature_tensor = self._get_raw_feature_as_tensor(key)
      self._feature_tensors[key] = feature_tensor
      return feature_tensor

    if not isinstance(key, (str, _FeatureColumn)):
      raise TypeError('"key" must be either a "str" or "_FeatureColumn". '
                      'Provided: {}'.format(key))

    if not isinstance(key, _FeatureColumn):
      raise ValueError('Feature {} is not in features dictionary.'.format(key))

    column = key
    logging.debug('Transforming feature_column %s.', column)
    transformed = column._transform_feature(self)  # pylint: disable=protected-access
    if transformed is None:
      raise ValueError('Column {} is not supported.'.format(column.name))
    self._feature_tensors[column] = transformed
    return transformed

  def _get_raw_feature_as_tensor(self, key):
    """Gets the raw_feature (keyed by `key`) as `tensor`.

    The raw feature is converted to (sparse) tensor and maybe expand dim.

    For both `Tensor` and `SparseTensor`, the rank will be expanded (to 2) if
    the rank is 1. This supports dynamic rank also. For rank 0 raw feature, will
    error out as it is not supported.

    Args:
      key: A `str` key to access the raw feature.

    Returns:
      A `Tensor` or `SparseTensor`.

    Raises:
      ValueError: if the raw feature has rank 0.
    """
    raw_feature = self._features[key]
    feature_tensor = sparse_tensor_lib.convert_to_tensor_or_sparse_tensor(
        raw_feature)

    def expand_dims(input_tensor):
      # Input_tensor must have rank 1.
      if isinstance(input_tensor, sparse_tensor_lib.SparseTensor):
        return sparse_ops.sparse_reshape(
            input_tensor, [array_ops.shape(input_tensor)[0], -1])
      else:
        return array_ops.expand_dims(input_tensor, -1)

    rank = feature_tensor.get_shape().ndims
    if rank is not None:
      if rank == 0:
        raise ValueError(
            'Feature (key: {}) cannot have rank 0. Give: {}'.format(
                key, feature_tensor))
      return feature_tensor if rank != 1 else expand_dims(feature_tensor)

    # Handle dynamic rank.
    with ops.control_dependencies([
        check_ops.assert_positive(
            array_ops.rank(feature_tensor),
            message='Feature (key: {}) cannot have rank 0. Given: {}'.format(
                key, feature_tensor))]):
      return control_flow_ops.cond(
          math_ops.equal(1, array_ops.rank(feature_tensor)),
          lambda: expand_dims(feature_tensor),
          lambda: feature_tensor)


# TODO(ptucker): Move to third_party/tensorflow/python/ops/sparse_ops.py
def _shape_offsets(shape):
  """Returns moving offset for each dimension given shape."""
  offsets = []
  for dim in reversed(shape):
    if offsets:
      offsets.append(dim * offsets[-1])
    else:
      offsets.append(dim)
  offsets.reverse()
  return offsets


# TODO(ptucker): Move to third_party/tensorflow/python/ops/sparse_ops.py
def _to_sparse_input(input_tensor, ignore_value=None):
  """Converts a `Tensor` to a `SparseTensor`, dropping ignore_value cells.

  If `input_tensor` is already a `SparseTensor`, just return it.

  Args:
    input_tensor: A string or integer `Tensor`.
    ignore_value: Entries in `dense_tensor` equal to this value will be
      absent from the resulting `SparseTensor`. If `None`, default value of
      `dense_tensor`'s dtype will be used ('' for `str`, -1 for `int`).

  Returns:
    A `SparseTensor` with the same shape as `input_tensor`.

  Raises:
    ValueError: when `input_tensor`'s rank is `None`.
  """
  input_tensor = sparse_tensor_lib.convert_to_tensor_or_sparse_tensor(
      input_tensor)
  if isinstance(input_tensor, sparse_tensor_lib.SparseTensor):
    return input_tensor
  with ops.name_scope(None, 'to_sparse_input', (input_tensor, ignore_value,)):
    if ignore_value is None:
      if input_tensor.dtype == dtypes.string:
        # Exception due to TF strings are converted to numpy objects by default.
        ignore_value = ''
      elif input_tensor.dtype.is_integer:
        ignore_value = -1  # -1 has a special meaning of missing feature
      else:
        # NOTE: `as_numpy_dtype` is a property, so with the parentheses this is
        # constructing a new numpy object of the given type, which yields the
        # default value for that type.
        ignore_value = input_tensor.dtype.as_numpy_dtype()
    ignore_value = math_ops.cast(
        ignore_value, input_tensor.dtype, name='ignore_value')
    indices = array_ops.where(
        math_ops.not_equal(input_tensor, ignore_value), name='indices')
    return sparse_tensor_lib.SparseTensor(
        indices=indices,
        values=array_ops.gather_nd(input_tensor, indices, name='values'),
        dense_shape=array_ops.shape(
            input_tensor, out_type=dtypes.int64, name='dense_shape'))


def _clean_feature_columns(feature_columns):
  """Verifies and normalizes `feature_columns` input."""
  if isinstance(feature_columns, _FeatureColumn):
    feature_columns = [feature_columns]

  if isinstance(feature_columns, collections.Iterator):
    feature_columns = list(feature_columns)

  if isinstance(feature_columns, dict):
    raise ValueError('Expected feature_columns to be iterable, found dict.')

  for column in feature_columns:
    if not isinstance(column, _FeatureColumn):
      raise ValueError('Items of feature_columns must be a _FeatureColumn. '
                       'Given (type {}): {}.'.format(type(column), column))
  if not feature_columns:
    raise ValueError('feature_columns must not be empty.')
  name_to_column = dict()
  for column in feature_columns:
    if column.name in name_to_column:
      raise ValueError('Duplicate feature column name found for columns: {} '
                       'and {}. This usually means that these columns refer to '
                       'same base feature. Either one must be discarded or a '
                       'duplicated but renamed item must be inserted in '
                       'features dict.'.format(column,
                                               name_to_column[column.name]))
    name_to_column[column.name] = column

  return feature_columns


class _NumericColumn(_DenseColumn,
                     collections.namedtuple('_NumericColumn', [
                         'key', 'shape', 'default_value', 'dtype',
                         'normalizer_fn'
                     ])):
  """see `numeric_column`."""

  @property
  def name(self):
    return self.key

  @property
  def _parse_example_spec(self):
    return {
        self.key:
            parsing_ops.FixedLenFeature(self.shape, self.dtype,
                                        self.default_value)
    }

  def _transform_feature(self, inputs):
    input_tensor = inputs.get(self.key)
    if isinstance(input_tensor, sparse_tensor_lib.SparseTensor):
      raise ValueError(
          'The corresponding Tensor of numerical column must be a Tensor. '
          'SparseTensor is not supported. key: {}'.format(self.key))
    if self.normalizer_fn is not None:
      input_tensor = self.normalizer_fn(input_tensor)
    return math_ops.to_float(input_tensor)

  @property
  def _variable_shape(self):
    return tensor_shape.TensorShape(self.shape)

  def _get_dense_tensor(self, inputs, weight_collections=None, trainable=None):
    """Returns dense `Tensor` representing numeric feature.

    Args:
      inputs: A `_LazyBuilder` object to access inputs.
      weight_collections: Unused `weight_collections` since no variables are
        created in this function.
      trainable: Unused `trainable` bool since no variables are created in
        this function.

    Returns:
      Dense `Tensor` created within `_transform_feature`.
    """
    # Do nothing with weight_collections and trainable since no variables are
    # created in this function.
    del weight_collections
    del trainable
    # Feature has been already transformed. Return the intermediate
    # representation created by _transform_feature.
    return inputs.get(self)


class _BucketizedColumn(_DenseColumn, _CategoricalColumn,
                        collections.namedtuple('_BucketizedColumn', [
                            'source_column', 'boundaries'])):
  """See `bucketized_column`."""

  @property
  def name(self):
    return '{}_bucketized'.format(self.source_column.name)

  @property
  def _parse_example_spec(self):
    return self.source_column._parse_example_spec  # pylint: disable=protected-access

  def _transform_feature(self, inputs):
    source_tensor = inputs.get(self.source_column)
    return math_ops._bucketize(  # pylint: disable=protected-access
        source_tensor,
        boundaries=self.boundaries)

  @property
  def _variable_shape(self):
    return tensor_shape.TensorShape(
        tuple(self.source_column.shape) + (len(self.boundaries) + 1,))

  def _get_dense_tensor(self, inputs, weight_collections=None, trainable=None):
    del weight_collections
    del trainable
    input_tensor = inputs.get(self)
    return array_ops.one_hot(
        indices=math_ops.to_int64(input_tensor),
        depth=len(self.boundaries) + 1,
        on_value=1.,
        off_value=0.)

  @property
  def _num_buckets(self):
    # By construction, source_column is always one-dimensional.
    return (len(self.boundaries) + 1) * self.source_column.shape[0]

  def _get_sparse_tensors(self, inputs, weight_collections=None,
                          trainable=None):
    input_tensor = inputs.get(self)
    batch_size = array_ops.shape(input_tensor)[0]
    # By construction, source_column is always one-dimensional.
    source_dimension = self.source_column.shape[0]

    i1 = array_ops.reshape(
        array_ops.tile(
            array_ops.expand_dims(math_ops.range(0, batch_size), 1),
            [1, source_dimension]),
        (-1,))
    i2 = array_ops.tile(math_ops.range(0, source_dimension), [batch_size])
    # Flatten the bucket indices and unique them across dimensions
    # E.g. 2nd dimension indices will range from k to 2*k-1 with k buckets
    bucket_indices = (
        array_ops.reshape(input_tensor, (-1,)) +
        (len(self.boundaries) + 1) * i2)

    indices = math_ops.to_int64(array_ops.transpose(array_ops.stack((i1, i2))))
    dense_shape = math_ops.to_int64(array_ops.stack(
        [batch_size, source_dimension]))
    sparse_tensor = sparse_tensor_lib.SparseTensor(
        indices=indices,
        values=bucket_indices,
        dense_shape=dense_shape)
    return _CategoricalColumn.IdWeightPair(sparse_tensor, None)


class _EmbeddingColumn(
    _DenseColumn,
    collections.namedtuple('_EmbeddingColumn', (
        'categorical_column', 'dimension', 'combiner', 'initializer',
        'ckpt_to_load_from', 'tensor_name_in_ckpt', 'max_norm', 'trainable'
    ))):
  """See `embedding_column`."""

  @property
  def name(self):
    if not hasattr(self, '_name'):
      self._name = '{}_embedding'.format(self.categorical_column.name)
    return self._name

  @property
  def _parse_example_spec(self):
    return self.categorical_column._parse_example_spec  # pylint: disable=protected-access

  def _transform_feature(self, inputs):
    return inputs.get(self.categorical_column)

  @property
  def _variable_shape(self):
    if not hasattr(self, '_shape'):
      self._shape = tensor_shape.vector(self.dimension)
    return self._shape

  def _get_dense_tensor(self, inputs, weight_collections=None, trainable=None):
    # Get sparse IDs and weights.
    sparse_tensors = self.categorical_column._get_sparse_tensors(  # pylint: disable=protected-access
        inputs, weight_collections=weight_collections, trainable=trainable)
    sparse_ids = sparse_tensors.id_tensor
    sparse_weights = sparse_tensors.weight_tensor

    embedding_shape = (self.categorical_column._num_buckets, self.dimension)  # pylint: disable=protected-access
    embedding_weights = variable_scope.get_variable(
        name='embedding_weights',
        shape=embedding_shape,
        dtype=dtypes.float32,
        initializer=self.initializer,
        trainable=self.trainable and trainable,
        collections=weight_collections)
    if self.ckpt_to_load_from is not None:
      to_restore = embedding_weights
      if isinstance(to_restore, variables.PartitionedVariable):
        to_restore = to_restore._get_variable_list()  # pylint: disable=protected-access
      checkpoint_utils.init_from_checkpoint(self.ckpt_to_load_from, {
          self.tensor_name_in_ckpt: to_restore
      })

    # Return embedding lookup result.
    return _safe_embedding_lookup_sparse(
        embedding_weights=embedding_weights,
        sparse_ids=sparse_ids,
        sparse_weights=sparse_weights,
        combiner=self.combiner,
        name='%s_weights' % self.name,
        max_norm=self.max_norm)


class _SharedEmbeddingColumn(
    _DenseColumn,
    collections.namedtuple('_SharedEmbeddingColumn', (
        'categorical_column', 'dimension', 'combiner', 'initializer',
        'shared_embedding_collection_name', 'ckpt_to_load_from',
        'tensor_name_in_ckpt', 'max_norm', 'trainable'
    ))):
  """See `embedding_column`."""

  @property
  def name(self):
    if not hasattr(self, '_name'):
      self._name = '{}_shared_embedding'.format(self.categorical_column.name)
    return self._name

  @property
  def _var_scope_name(self):
    return self.shared_embedding_collection_name

  @property
  def _parse_example_spec(self):
    return self.categorical_column._parse_example_spec  # pylint: disable=protected-access

  def _transform_feature(self, inputs):
    return inputs.get(self.categorical_column)

  @property
  def _variable_shape(self):
    if not hasattr(self, '_shape'):
      self._shape = tensor_shape.vector(self.dimension)
    return self._shape

  def _get_dense_tensor(self, inputs, weight_collections=None, trainable=None):
    # This method is called from a variable_scope with name _var_scope_name,
    # which is shared among all shared embeddings. Open a name_scope here, so
    # that the ops for different columns have distinct names.
    with ops.name_scope(None, default_name=self.name):
      # Get sparse IDs and weights.
      sparse_tensors = self.categorical_column._get_sparse_tensors(  # pylint: disable=protected-access
          inputs, weight_collections=weight_collections, trainable=trainable)
      sparse_ids = sparse_tensors.id_tensor
      sparse_weights = sparse_tensors.weight_tensor

      embedding_shape = (self.categorical_column._num_buckets, self.dimension)  # pylint: disable=protected-access
      shared_embedding_collection = ops.get_collection(
          self.shared_embedding_collection_name)
      if shared_embedding_collection:
        if len(shared_embedding_collection) > 1:
          raise ValueError(
              'Collection {} can only contain one variable. '
              'Suggested fix A: Choose a unique name for this collection. '
              'Suggested fix B: Do not add any variables to this collection. '
              'The feature_column library already adds a variable under the '
              'hood.'.format(shared_embedding_collection))
        embedding_weights = shared_embedding_collection[0]
        if embedding_weights.get_shape() != embedding_shape:
          raise ValueError(
              'Shared embedding collection {} contains variable {} of '
              'unexpected shape {}. Expected shape is {}. '
              'Suggested fix A: Choose a unique name for this collection. '
              'Suggested fix B: Do not add any variables to this collection. '
              'The feature_column library already adds a variable under the '
              'hood.'.format(
                  self.shared_embedding_collection_name, embedding_weights.name,
                  embedding_weights.get_shape(), embedding_shape))
      else:
        embedding_weights = variable_scope.get_variable(
            name='embedding_weights',
            shape=embedding_shape,
            dtype=dtypes.float32,
            initializer=self.initializer,
            trainable=self.trainable and trainable,
            collections=weight_collections)
        ops.add_to_collection(
            self.shared_embedding_collection_name, embedding_weights)
      if self.ckpt_to_load_from is not None:
        to_restore = embedding_weights
        if isinstance(to_restore, variables.PartitionedVariable):
          to_restore = to_restore._get_variable_list()  # pylint: disable=protected-access
        checkpoint_utils.init_from_checkpoint(self.ckpt_to_load_from, {
            self.tensor_name_in_ckpt: to_restore
        })

      # Return embedding lookup result.
      return _safe_embedding_lookup_sparse(
          embedding_weights=embedding_weights,
          sparse_ids=sparse_ids,
          sparse_weights=sparse_weights,
          combiner=self.combiner,
          name='%s_weights' % self.name,
          max_norm=self.max_norm)


def _create_tuple(shape, value):
  """Returns a tuple with given shape and filled with value."""
  if shape:
    return tuple([_create_tuple(shape[1:], value) for _ in range(shape[0])])
  return value


def _as_tuple(value):
  if not nest.is_sequence(value):
    return value
  return tuple([_as_tuple(v) for v in value])


def _check_shape(shape, key):
  """Returns shape if it's valid, raises error otherwise."""
  assert shape is not None
  if not nest.is_sequence(shape):
    shape = [shape]
  shape = tuple(shape)
  for dimension in shape:
    if not isinstance(dimension, int):
      raise TypeError('shape dimensions must be integer. '
                      'shape: {}, key: {}'.format(shape, key))
    if dimension < 1:
      raise ValueError('shape dimensions must be greater than 0. '
                       'shape: {}, key: {}'.format(shape, key))
  return shape


def _is_shape_and_default_value_compatible(default_value, shape):
  """Verifies compatibility of shape and default_value."""
  # Invalid condition:
  #  * if default_value is not a scalar and shape is empty
  #  * or if default_value is an iterable and shape is not empty
  if nest.is_sequence(default_value) != bool(shape):
    return False
  if not shape:
    return True
  if len(default_value) != shape[0]:
    return False
  for i in range(shape[0]):
    if not _is_shape_and_default_value_compatible(default_value[i], shape[1:]):
      return False
  return True


def _check_default_value(shape, default_value, dtype, key):
  """Returns default value as tuple if it's valid, otherwise raises errors.

  This function verifies that `default_value` is compatible with both `shape`
  and `dtype`. If it is not compatible, it raises an error. If it is compatible,
  it casts default_value to a tuple and returns it. `key` is used only
  for error message.

  Args:
    shape: An iterable of integers specifies the shape of the `Tensor`.
    default_value: If a single value is provided, the same value will be applied
      as the default value for every item. If an iterable of values is
      provided, the shape of the `default_value` should be equal to the given
      `shape`.
    dtype: defines the type of values. Default value is `tf.float32`. Must be a
      non-quantized, real integer or floating point type.
    key: Column name, used only for error messages.

  Returns:
    A tuple which will be used as default value.

  Raises:
    TypeError: if `default_value` is an iterable but not compatible with `shape`
    TypeError: if `default_value` is not compatible with `dtype`.
    ValueError: if `dtype` is not convertible to `tf.float32`.
  """
  if default_value is None:
    return None

  if isinstance(default_value, int):
    return _create_tuple(shape, default_value)

  if isinstance(default_value, float) and dtype.is_floating:
    return _create_tuple(shape, default_value)

  if callable(getattr(default_value, 'tolist', None)):  # Handles numpy arrays
    default_value = default_value.tolist()

  if nest.is_sequence(default_value):
    if not _is_shape_and_default_value_compatible(default_value, shape):
      raise ValueError(
          'The shape of default_value must be equal to given shape. '
          'default_value: {}, shape: {}, key: {}'.format(
              default_value, shape, key))
    # Check if the values in the list are all integers or are convertible to
    # floats.
    is_list_all_int = all(
        isinstance(v, int) for v in nest.flatten(default_value))
    is_list_has_float = any(
        isinstance(v, float) for v in nest.flatten(default_value))
    if is_list_all_int:
      return _as_tuple(default_value)
    if is_list_has_float and dtype.is_floating:
      return _as_tuple(default_value)
  raise TypeError('default_value must be compatible with dtype. '
                  'default_value: {}, dtype: {}, key: {}'.format(
                      default_value, dtype, key))


class _HashedCategoricalColumn(
    _CategoricalColumn,
    collections.namedtuple('_HashedCategoricalColumn',
                           ['key', 'hash_bucket_size', 'dtype'])):
  """see `categorical_column_with_hash_bucket`."""

  @property
  def name(self):
    return self.key

  @property
  def _parse_example_spec(self):
    return {self.key: parsing_ops.VarLenFeature(self.dtype)}

  def _transform_feature(self, inputs):
    input_tensor = _to_sparse_input(inputs.get(self.key))
    if not isinstance(input_tensor, sparse_tensor_lib.SparseTensor):
      raise ValueError('SparseColumn input must be a SparseTensor.')

    _assert_string_or_int(
        input_tensor.dtype,
        prefix='column_name: {} input_tensor'.format(self.key))

    if self.dtype.is_integer != input_tensor.dtype.is_integer:
      raise ValueError(
          'Column dtype and SparseTensors dtype must be compatible. '
          'key: {}, column dtype: {}, tensor dtype: {}'.format(
              self.key, self.dtype, input_tensor.dtype))

    if self.dtype == dtypes.string:
      sparse_values = input_tensor.values
    else:
      sparse_values = string_ops.as_string(input_tensor.values)

    sparse_id_values = string_ops.string_to_hash_bucket_fast(
        sparse_values, self.hash_bucket_size, name='lookup')
    return sparse_tensor_lib.SparseTensor(
        input_tensor.indices, sparse_id_values, input_tensor.dense_shape)

  @property
  def _num_buckets(self):
    """Returns number of buckets in this sparse feature."""
    return self.hash_bucket_size

  def _get_sparse_tensors(self, inputs, weight_collections=None,
                          trainable=None):
    return _CategoricalColumn.IdWeightPair(inputs.get(self), None)


class _VocabularyFileCategoricalColumn(
    _CategoricalColumn,
    collections.namedtuple('_VocabularyFileCategoricalColumn', (
        'key', 'vocabulary_file', 'vocabulary_size', 'num_oov_buckets', 'dtype',
        'default_value'
    ))):
  """See `categorical_column_with_vocabulary_file`."""

  @property
  def name(self):
    return self.key

  @property
  def _parse_example_spec(self):
    return {self.key: parsing_ops.VarLenFeature(self.dtype)}

  def _transform_feature(self, inputs):
    input_tensor = _to_sparse_input(inputs.get(self.key))

    if self.dtype.is_integer != input_tensor.dtype.is_integer:
      raise ValueError(
          'Column dtype and SparseTensors dtype must be compatible. '
          'key: {}, column dtype: {}, tensor dtype: {}'.format(
              self.key, self.dtype, input_tensor.dtype))

    _assert_string_or_int(
        input_tensor.dtype,
        prefix='column_name: {} input_tensor'.format(self.key))

    key_dtype = self.dtype
    if input_tensor.dtype.is_integer:
      # `index_table_from_file` requires 64-bit integer keys.
      key_dtype = dtypes.int64
      input_tensor = math_ops.to_int64(input_tensor)

    return lookup_ops.index_table_from_file(
        vocabulary_file=self.vocabulary_file,
        num_oov_buckets=self.num_oov_buckets,
        vocab_size=self.vocabulary_size,
        default_value=self.default_value,
        key_dtype=key_dtype,
        name='{}_lookup'.format(self.key)).lookup(input_tensor)

  @property
  def _num_buckets(self):
    """Returns number of buckets in this sparse feature."""
    return self.vocabulary_size + self.num_oov_buckets

  def _get_sparse_tensors(
      self, inputs, weight_collections=None, trainable=None):
    return _CategoricalColumn.IdWeightPair(inputs.get(self), None)


class _VocabularyListCategoricalColumn(
    _CategoricalColumn,
    collections.namedtuple('_VocabularyListCategoricalColumn', (
        'key', 'vocabulary_list', 'dtype', 'default_value', 'num_oov_buckets'
    ))):
  """See `categorical_column_with_vocabulary_list`."""

  @property
  def name(self):
    return self.key

  @property
  def _parse_example_spec(self):
    return {self.key: parsing_ops.VarLenFeature(self.dtype)}

  def _transform_feature(self, inputs):
    input_tensor = _to_sparse_input(inputs.get(self.key))

    if self.dtype.is_integer != input_tensor.dtype.is_integer:
      raise ValueError(
          'Column dtype and SparseTensors dtype must be compatible. '
          'key: {}, column dtype: {}, tensor dtype: {}'.format(
              self.key, self.dtype, input_tensor.dtype))

    _assert_string_or_int(
        input_tensor.dtype,
        prefix='column_name: {} input_tensor'.format(self.key))

    key_dtype = self.dtype
    if input_tensor.dtype.is_integer:
      # `index_table_from_tensor` requires 64-bit integer keys.
      key_dtype = dtypes.int64
      input_tensor = math_ops.to_int64(input_tensor)

    return lookup_ops.index_table_from_tensor(
        vocabulary_list=tuple(self.vocabulary_list),
        default_value=self.default_value,
        num_oov_buckets=self.num_oov_buckets,
        dtype=key_dtype,
        name='{}_lookup'.format(self.key)).lookup(input_tensor)

  @property
  def _num_buckets(self):
    """Returns number of buckets in this sparse feature."""
    return len(self.vocabulary_list) + self.num_oov_buckets

  def _get_sparse_tensors(
      self, inputs, weight_collections=None, trainable=None):
    return _CategoricalColumn.IdWeightPair(inputs.get(self), None)


class _IdentityCategoricalColumn(
    _CategoricalColumn,
    collections.namedtuple('_IdentityCategoricalColumn', (
        'key', 'num_buckets', 'default_value'
    ))):

  """See `categorical_column_with_identity`."""

  @property
  def name(self):
    return self.key

  @property
  def _parse_example_spec(self):
    return {self.key: parsing_ops.VarLenFeature(dtypes.int64)}

  def _transform_feature(self, inputs):
    input_tensor = _to_sparse_input(inputs.get(self.key))

    if not input_tensor.dtype.is_integer:
      raise ValueError(
          'Invalid input, not integer. key: {} dtype: {}'.format(
              self.key, input_tensor.dtype))

    values = math_ops.to_int64(input_tensor.values, name='values')
    num_buckets = math_ops.to_int64(self.num_buckets, name='num_buckets')
    zero = math_ops.to_int64(0, name='zero')
    if self.default_value is None:
      # Fail if values are out-of-range.
      assert_less = check_ops.assert_less(
          values, num_buckets, data=(values, num_buckets),
          name='assert_less_than_num_buckets')
      assert_greater = check_ops.assert_greater_equal(
          values, zero, data=(values,),
          name='assert_greater_or_equal_0')
      with ops.control_dependencies((assert_less, assert_greater)):
        values = array_ops.identity(values)
    else:
      # Assign default for out-of-range values.
      values = array_ops.where(
          math_ops.logical_or(
              values < zero, values >= num_buckets, name='out_of_range'),
          array_ops.fill(
              dims=array_ops.shape(values),
              value=math_ops.to_int64(self.default_value),
              name='default_values'),
          values)

    return sparse_tensor_lib.SparseTensor(
        indices=input_tensor.indices,
        values=values,
        dense_shape=input_tensor.dense_shape)

  @property
  def _num_buckets(self):
    """Returns number of buckets in this sparse feature."""
    return self.num_buckets

  def _get_sparse_tensors(
      self, inputs, weight_collections=None, trainable=None):
    return _CategoricalColumn.IdWeightPair(inputs.get(self), None)


class _WeightedCategoricalColumn(
    _CategoricalColumn,
    collections.namedtuple('_WeightedCategoricalColumn', (
        'categorical_column', 'weight_feature_key', 'dtype'
    ))):
  """See `weighted_categorical_column`."""

  @property
  def name(self):
    return '{}_weighted_by_{}'.format(
        self.categorical_column.name, self.weight_feature_key)

  @property
  def _parse_example_spec(self):
    config = self.categorical_column._parse_example_spec  # pylint: disable=protected-access
    if self.weight_feature_key in config:
      raise ValueError('Parse config {} already exists for {}.'.format(
          config[self.weight_feature_key], self.weight_feature_key))
    config[self.weight_feature_key] = parsing_ops.VarLenFeature(self.dtype)
    return config

  @property
  def _num_buckets(self):
    return self.categorical_column._num_buckets  # pylint: disable=protected-access

  def _transform_feature(self, inputs):
    weight_tensor = inputs.get(self.weight_feature_key)
    if weight_tensor is None:
      raise ValueError('Missing weights {}.'.format(self.weight_feature_key))
    weight_tensor = sparse_tensor_lib.convert_to_tensor_or_sparse_tensor(
        weight_tensor)
    if self.dtype != weight_tensor.dtype.base_dtype:
      raise ValueError('Bad dtype, expected {}, but got {}.'.format(
          self.dtype, weight_tensor.dtype))
    if not isinstance(weight_tensor, sparse_tensor_lib.SparseTensor):
      # The weight tensor can be a regular Tensor. In this case, sparsify it.
      weight_tensor = _to_sparse_input(weight_tensor, ignore_value=0.0)
    if not weight_tensor.dtype.is_floating:
      weight_tensor = math_ops.to_float(weight_tensor)
    return (inputs.get(self.categorical_column), weight_tensor)

  def _get_sparse_tensors(
      self, inputs, weight_collections=None, trainable=None):
    del weight_collections
    del trainable
    tensors = inputs.get(self)
    return _CategoricalColumn.IdWeightPair(tensors[0], tensors[1])


class _CrossedColumn(
    _CategoricalColumn,
    collections.namedtuple('_CrossedColumn',
                           ['keys', 'hash_bucket_size', 'hash_key'])):
  """See `crossed_column`."""

  @property
  def name(self):
    feature_names = []
    for key in _collect_leaf_level_keys(self):
      if isinstance(key, _FeatureColumn):
        feature_names.append(key.name)
      else:  # key must be a string
        feature_names.append(key)
    return '_X_'.join(sorted(feature_names))

  @property
  def _parse_example_spec(self):
    config = {}
    for key in self.keys:
      if isinstance(key, _FeatureColumn):
        config.update(key._parse_example_spec)  # pylint: disable=protected-access
      else:  # key must be a string
        config.update({key: parsing_ops.VarLenFeature(dtypes.string)})
    return config

  def _transform_feature(self, inputs):
    feature_tensors = []
    for key in _collect_leaf_level_keys(self):
      if isinstance(key, six.string_types):
        feature_tensors.append(inputs.get(key))
      elif isinstance(key, _CategoricalColumn):
        ids_and_weights = key._get_sparse_tensors(inputs)  # pylint: disable=protected-access
        if ids_and_weights.weight_tensor is not None:
          raise ValueError(
              'crossed_column does not support weight_tensor, but the given '
              'column populates weight_tensor. '
              'Given column: {}'.format(key.name))
        feature_tensors.append(ids_and_weights.id_tensor)
      else:
        raise ValueError('Unsupported column type. Given: {}'.format(key))
    return sparse_ops._sparse_cross_hashed(  # pylint: disable=protected-access
        inputs=feature_tensors,
        num_buckets=self.hash_bucket_size,
        hash_key=self.hash_key)

  @property
  def _num_buckets(self):
    """Returns number of buckets in this sparse feature."""
    return self.hash_bucket_size

  def _get_sparse_tensors(self, inputs, weight_collections=None,
                          trainable=None):
    return _CategoricalColumn.IdWeightPair(inputs.get(self), None)


def _collect_leaf_level_keys(cross):
  """Collects base keys by expanding all nested crosses.

  Args:
    cross: A `_CrossedColumn`.

  Returns:
    A list of strings or `_CategoricalColumn` instances.
  """
  leaf_level_keys = []
  for k in cross.keys:
    if isinstance(k, _CrossedColumn):
      leaf_level_keys.extend(_collect_leaf_level_keys(k))
    else:
      leaf_level_keys.append(k)
  return leaf_level_keys


# TODO(zakaria): Move this to embedding_ops and make it public.
def _safe_embedding_lookup_sparse(embedding_weights,
                                  sparse_ids,
                                  sparse_weights=None,
                                  combiner='mean',
                                  default_id=None,
                                  name=None,
                                  partition_strategy='div',
                                  max_norm=None):
  """Lookup embedding results, accounting for invalid IDs and empty features.

  The partitioned embedding in `embedding_weights` must all be the same shape
  except for the first dimension. The first dimension is allowed to vary as the
  vocabulary size is not necessarily a multiple of `P`.  `embedding_weights`
  may be a `PartitionedVariable` as returned by using `tf.get_variable()` with a
  partitioner.

  Invalid IDs (< 0) are pruned from input IDs and weights, as well as any IDs
  with non-positive weight. For an entry with no features, the embedding vector
  for `default_id` is returned, or the 0-vector if `default_id` is not supplied.

  The ids and weights may be multi-dimensional. Embeddings are always aggregated
  along the last dimension.

  Args:
    embedding_weights:  A list of `P` float `Tensor`s or values representing
        partitioned embedding `Tensor`s.  Alternatively, a `PartitionedVariable`
        created by partitioning along dimension 0.  The total unpartitioned
        shape should be `[e_0, e_1, ..., e_m]`, where `e_0` represents the
        vocab size and `e_1, ..., e_m` are the embedding dimensions.
    sparse_ids: `SparseTensor` of shape `[d_0, d_1, ..., d_n]` containing the
        ids. `d_0` is typically batch size.
    sparse_weights: `SparseTensor` of same shape as `sparse_ids`, containing
        float weights corresponding to `sparse_ids`, or `None` if all weights
        are be assumed to be 1.0.
    combiner: A string specifying how to combine embedding results for each
        entry. Currently "mean", "sqrtn" and "sum" are supported, with "mean"
        the default.
    default_id: The id to use for an entry with no features.
    name: A name for this operation (optional).
    partition_strategy: A string specifying the partitioning strategy.
        Currently `"div"` and `"mod"` are supported. Default is `"div"`.
    max_norm: If not `None`, all embeddings are l2-normalized to max_norm before
        combining.


  Returns:
    Dense `Tensor` of shape `[d_0, d_1, ..., d_{n-1}, e_1, ..., e_m]`.

  Raises:
    ValueError: if `embedding_weights` is empty.
  """
  if embedding_weights is None:
    raise ValueError('Missing embedding_weights %s.' % embedding_weights)
  if isinstance(embedding_weights, variables.PartitionedVariable):
    embedding_weights = list(embedding_weights)  # get underlying Variables.
  if not isinstance(embedding_weights, list):
    embedding_weights = [embedding_weights]
  if len(embedding_weights) < 1:
    raise ValueError('Missing embedding_weights %s.' % embedding_weights)

  dtype = sparse_weights.dtype if sparse_weights is not None else None
  embedding_weights = [
      ops.convert_to_tensor(w, dtype=dtype) for w in embedding_weights
  ]

  with ops.name_scope(name, 'embedding_lookup',
                      embedding_weights + [sparse_ids,
                                           sparse_weights]) as scope:
    # Reshape higher-rank sparse ids and weights to linear segment ids.
    original_shape = sparse_ids.dense_shape
    original_rank_dim = sparse_ids.dense_shape.get_shape()[0]
    original_rank = (
        array_ops.size(original_shape)
        if original_rank_dim.value is None
        else original_rank_dim.value)
    sparse_ids = sparse_ops.sparse_reshape(sparse_ids, [
        math_ops.reduce_prod(
            array_ops.slice(original_shape, [0], [original_rank - 1])),
        array_ops.gather(original_shape, original_rank - 1)])
    if sparse_weights is not None:
      sparse_weights = sparse_tensor_lib.SparseTensor(
          sparse_ids.indices,
          sparse_weights.values, sparse_ids.dense_shape)

    # Prune invalid ids and weights.
    sparse_ids, sparse_weights = _prune_invalid_ids(sparse_ids, sparse_weights)

    # Fill in dummy values for empty features, if necessary.
    sparse_ids, is_row_empty = sparse_ops.sparse_fill_empty_rows(sparse_ids,
                                                                 default_id or
                                                                 0)
    if sparse_weights is not None:
      sparse_weights, _ = sparse_ops.sparse_fill_empty_rows(sparse_weights, 1.0)

    result = embedding_ops.embedding_lookup_sparse(
        embedding_weights,
        sparse_ids,
        sparse_weights,
        combiner=combiner,
        partition_strategy=partition_strategy,
        name=None if default_id is None else scope,
        max_norm=max_norm)

    if default_id is None:
      # Broadcast is_row_empty to the same shape as embedding_lookup_result,
      # for use in Select.
      is_row_empty = array_ops.tile(
          array_ops.reshape(is_row_empty, [-1, 1]),
          array_ops.stack([1, array_ops.shape(result)[1]]))

      result = array_ops.where(is_row_empty,
                               array_ops.zeros_like(result),
                               result,
                               name=scope)

    # Reshape back from linear ids back into higher-dimensional dense result.
    final_result = array_ops.reshape(
        result,
        array_ops.concat([
            array_ops.slice(
                math_ops.cast(original_shape, dtypes.int32), [0],
                [original_rank - 1]),
            array_ops.slice(array_ops.shape(result), [1], [-1])
        ], 0))
    final_result.set_shape(tensor_shape.unknown_shape(
        (original_rank_dim - 1).value).concatenate(result.get_shape()[1:]))
    return final_result


def _prune_invalid_ids(sparse_ids, sparse_weights):
  """Prune invalid IDs (< 0) from the input ids and weights."""
  is_id_valid = math_ops.greater_equal(sparse_ids.values, 0)
  if sparse_weights is not None:
    is_id_valid = math_ops.logical_and(
        is_id_valid, math_ops.greater(sparse_weights.values, 0))
  sparse_ids = sparse_ops.sparse_retain(sparse_ids, is_id_valid)
  if sparse_weights is not None:
    sparse_weights = sparse_ops.sparse_retain(sparse_weights, is_id_valid)
  return sparse_ids, sparse_weights


class _IndicatorColumn(_DenseColumn,
                       collections.namedtuple('_IndicatorColumn',
                                              ['categorical_column'])):
  """Represents a one-hot column for use in deep networks.

  Args:
    categorical_column: A `_CategoricalColumn` which is created by
      `categorical_column_with_*` function.
  """

  @property
  def name(self):
    return '{}_indicator'.format(self.categorical_column.name)

  def _transform_feature(self, inputs):
    """Returns dense `Tensor` representing feature.

    Args:
      inputs: A `_LazyBuilder` object to access inputs.

    Returns:
      Transformed feature `Tensor`.

    Raises:
      ValueError: if input rank is not known at graph building time.
    """
    id_weight_pair = self.categorical_column._get_sparse_tensors(inputs)  # pylint: disable=protected-access
    id_tensor = id_weight_pair.id_tensor
    weight_tensor = id_weight_pair.weight_tensor

    # If the underlying column is weighted, return the input as a dense tensor.
    if weight_tensor is not None:
      weighted_column = sparse_ops.sparse_merge(
          sp_ids=id_tensor,
          sp_values=weight_tensor,
          vocab_size=int(self._variable_shape[-1]))
      # Remove (?, -1) index
      weighted_column = sparse_ops.sparse_slice(weighted_column, [0, 0],
                                                weighted_column.dense_shape)
      return sparse_ops.sparse_tensor_to_dense(weighted_column)

    dense_id_tensor = sparse_ops.sparse_tensor_to_dense(
        id_tensor, default_value=-1)

    # One hot must be float for tf.concat reasons since all other inputs to
    # input_layer are float32.
    one_hot_id_tensor = array_ops.one_hot(
        dense_id_tensor,
        depth=self._variable_shape[-1],
        on_value=1.0,
        off_value=0.0)

    # Reduce to get a multi-hot per example.
    return math_ops.reduce_sum(one_hot_id_tensor, axis=[-2])

  @property
  def _parse_example_spec(self):
    return self.categorical_column._parse_example_spec  # pylint: disable=protected-access

  @property
  def _variable_shape(self):
    """Returns a `TensorShape` representing the shape of the dense `Tensor`."""
    return tensor_shape.TensorShape([1, self.categorical_column._num_buckets])  # pylint: disable=protected-access

  def _get_dense_tensor(self, inputs, weight_collections=None, trainable=None):
    """Returns dense `Tensor` representing feature.

    Args:
      inputs: A `_LazyBuilder` object to access inputs.
      weight_collections: Unused `weight_collections` since no variables are
        created in this function.
      trainable: Unused `trainable` bool since no variables are created in
        this function.

    Returns:
      Dense `Tensor` created within `_transform_feature`.
    """
    # Do nothing with weight_collections and trainable since no variables are
    # created in this function.
    del weight_collections
    del trainable
    # Feature has been already transformed. Return the intermediate
    # representation created by _transform_feature.
    return inputs.get(self)


def _verify_static_batch_size_equality(tensors, columns):
  # bath_size is a tf.Dimension object.
  expected_batch_size = None
  for i in range(0, len(tensors)):
    if tensors[i].shape[0].value is not None:
      if expected_batch_size is None:
        bath_size_column_index = i
        expected_batch_size = tensors[i].shape[0]
      elif not expected_batch_size.is_compatible_with(tensors[i].shape[0]):
        raise ValueError(
            'Batch size (first dimension) of each feature must be same. '
            'Batch size of columns ({}, {}): ({}, {})'.format(
                columns[bath_size_column_index].name, columns[i].name,
                expected_batch_size, tensors[i].shape[0]))