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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_columns. To be specific, assume the input as SparseTensor looks like:

  shape = [2, 2]
      [0, 0]: "a"
      [1, 0]: "b"
      [1, 1]: "c"

linear_model assigns weights for the presence of "a", "b", "c' implicitly, just like indicator_column, while input_layer explicitly requires wrapping each of categorical columns with an embedding_column or an indicator_column.

Example of usage:

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 =, features=make_parse_example_spec(columns))
prediction = linear_model(features, columns)

The sparse_combiner argument works as follows For example, for two features represented as the categorical columns:

  # Feature 1

  shape = [2, 2]
      [0, 0]: "a"
      [0, 1]: "b"
      [1, 0]: "c"

  # Feature 2

  shape = [2, 3]
      [0, 0]: "d"
      [1, 0]: "e"
      [1, 1]: "f"
      [1, 2]: "f"

with sparse_combiner as "mean", the linear model outputs consequently are:

  y_0 = 1.0 / 2.0 * ( w_a + w_b ) + w_d + b
  y_1 = w_c + 1.0 / 3.0 * ( w_e + 2.0 * w_f ) + b

where y_i is the output, b is the bias, and w_x is the weight assigned to the presence of x in the input features.

features A mapping from key to tensors. _FeatureColumns 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 _FeatureColumns.
units An integer, dimensionality of the output space. Default value is 1.
sparse_combiner A string specifying how to reduce if a categorical column is multivalent. Except numeric_column, almost all columns passed to linear_model are considered as categorical columns. It combines each categorical column independently. Currently "mean", "sqrtn" and "sum" are supported, with "sum" the default for linear model. "sqrtn" often achieves good accuracy, in particular with bag-of-words columns.

  • "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 Variables. For example, after the call, we might have cols_to_vars = { _NumericColumn( key='numeric_feature1', shape=(1,): [], 'bias': [], _NumericColumn( key='numeric_feature2', shape=(2,)): []} 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.

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

ValueError if an item in feature_columns is neither a _DenseColumn nor _CategoricalColumn.