In the previous TensorFlow Linear Model Tutorial, we trained a logistic regression model to predict the probability that the individual has an annual income of over 50,000 dollars using the Census Income Dataset. TensorFlow is great for training deep neural networks too, and you might be thinking which one you should choose—Well, why not both? Would it be possible to combine the strengths of both in one model?
In this tutorial, we'll introduce how to use the tf.estimator API to jointly train a wide linear model and a deep feedforward neural network. This approach combines the strengths of memorization and generalization. It's useful for generic largescale regression and classification problems with sparse input features (e.g., categorical features with a large number of possible feature values). If you're interested in learning more about how Wide & Deep Learning works, please check out our research paper.
The figure above shows a comparison of a wide model (logistic regression with sparse features and transformations), a deep model (feedforward neural network with an embedding layer and several hidden layers), and a Wide & Deep model (joint training of both). At a high level, there are only 3 steps to configure a wide, deep, or Wide & Deep model using the tf.estimator API:
 Select features for the wide part: Choose the sparse base columns and crossed columns you want to use.
 Select features for the deep part: Choose the continuous columns, the embedding dimension for each categorical column, and the hidden layer sizes.
 Put them all together in a Wide & Deep model
(
DNNLinearCombinedClassifier
).
And that's it! Let's go through a simple example.
Setup
To try the code for this tutorial:

Install TensorFlow if you haven't already.

Download the tutorial code.

Install the pandas data analysis library. tf.estimator doesn't require pandas, but it does support it, and this tutorial uses pandas. To install pandas:
a. Get
pip
:# Ubuntu/Linux 64bit $ sudo aptget install pythonpip pythondev # Mac OS X $ sudo easy_install pip $ sudo easy_install upgrade six
b. Use
pip
to install pandas:$ sudo pip install pandas
If you have trouble installing pandas, consult the instructions on the pandas site.

Execute the tutorial code with the following command to train the linear model described in this tutorial:
$ python wide_n_deep_tutorial.py model_type=wide_n_deep
Read on to find out how this code builds its linear model.
Define Base Feature Columns
First, let's define the base categorical and continuous feature columns that we'll use. These base columns will be the building blocks used by both the wide part and the deep part of the model.
import tensorflow as tf
gender = tf.feature_column.categorical_column_with_vocabulary_list(
"gender", ["Female", "Male"])
education = tf.feature_column.categorical_column_with_vocabulary_list(
"education", [
"Bachelors", "HSgrad", "11th", "Masters", "9th",
"Somecollege", "Assocacdm", "Assocvoc", "7th8th",
"Doctorate", "Profschool", "5th6th", "10th", "1st4th",
"Preschool", "12th"
])
tf.feature_column.categorical_column_with_vocabulary_list(
"marital_status", [
"Marriedcivspouse", "Divorced", "Marriedspouseabsent",
"Nevermarried", "Separated", "MarriedAFspouse", "Widowed"
])
relationship = tf.feature_column.categorical_column_with_vocabulary_list(
"relationship", [
"Husband", "Notinfamily", "Wife", "Ownchild", "Unmarried",
"Otherrelative"
])
workclass = tf.feature_column.categorical_column_with_vocabulary_list(
"workclass", [
"Selfempnotinc", "Private", "Stategov", "Federalgov",
"Localgov", "?", "Selfempinc", "Withoutpay", "Neverworked"
])
# To show an example of hashing:
occupation = tf.feature_column.categorical_column_with_hash_bucket(
"occupation", hash_bucket_size=1000)
native_country = tf.feature_column.categorical_column_with_hash_bucket(
"native_country", hash_bucket_size=1000)
# Continuous base columns.
age = tf.feature_column.numeric_column("age")
education_num = tf.feature_column.numeric_column("education_num")
capital_gain = tf.feature_column.numeric_column("capital_gain")
capital_loss = tf.feature_column.numeric_column("capital_loss")
hours_per_week = tf.feature_column.numeric_column("hours_per_week")
# Transformations.
age_buckets = tf.feature_column.bucketized_column(
age, boundaries=[18, 25, 30, 35, 40, 45, 50, 55, 60, 65])
The Wide Model: Linear Model with Crossed Feature Columns
The wide model is a linear model with a wide set of sparse and crossed feature columns:
base_columns = [
gender, native_country, education, occupation, workclass, relationship,
age_buckets,
]
crossed_columns = [
tf.feature_column.crossed_column(
["education", "occupation"], hash_bucket_size=1000),
tf.feature_column.crossed_column(
[age_buckets, "education", "occupation"], hash_bucket_size=1000),
tf.feature_column.crossed_column(
["native_country", "occupation"], hash_bucket_size=1000)
]
Wide models with crossed feature columns can memorize sparse interactions between features effectively. That being said, one limitation of crossed feature columns is that they do not generalize to feature combinations that have not appeared in the training data. Let's add a deep model with embeddings to fix that.
The Deep Model: Neural Network with Embeddings
The deep model is a feedforward neural network, as shown in the previous figure. Each of the sparse, highdimensional categorical features are first converted into a lowdimensional and dense realvalued vector, often referred to as an embedding vector. These lowdimensional dense embedding vectors are concatenated with the continuous features, and then fed into the hidden layers of a neural network in the forward pass. The embedding values are initialized randomly, and are trained along with all other model parameters to minimize the training loss. If you're interested in learning more about embeddings, check out the TensorFlow tutorial on Vector Representations of Words, or Word Embedding on Wikipedia.
Another way to represent categorical columns to feed into a neural network is
via a multihot representation. This is often appropriate for categorical
columns with only a few possible values. E.g. for the gender column, "Male"
can be represented as [1, 0]
and "Female"
as [0, 1]
. This is a fixed
representation, whereas embeddings are more flexible and calculated at training
time.
We'll configure the embeddings for the categorical columns using
embedding_column
, and concatenate them with the continuous columns.
We also use indicator_column
to create multihot representation of some
categorical columns.
deep_columns = [
tf.feature_column.indicator_column(workclass),
tf.feature_column.indicator_column(education),
tf.feature_column.indicator_column(gender),
tf.feature_column.indicator_column(relationship),
# To show an example of embedding
tf.feature_column.embedding_column(native_country, dimension=8),
tf.feature_column.embedding_column(occupation, dimension=8),
age,
education_num,
capital_gain,
capital_loss,
hours_per_week,
]
The higher the dimension
of the embedding is, the more degrees of freedom the
model will have to learn the representations of the features. For simplicity, we
set the dimension to 8 for all feature columns here. Empirically, a more
informed decision for the number of dimensions is to start with a value on the
order of \(\log_2(n)\) or \(k\sqrt[4]n\), where \(n\) is the number of
unique features in a feature column and \(k\) is a small constant (usually
smaller than 10).
Through dense embeddings, deep models can generalize better and make predictions on feature pairs that were previously unseen in the training data. However, it is difficult to learn effective lowdimensional representations for feature columns when the underlying interaction matrix between two feature columns is sparse and highrank. In such cases, the interaction between most feature pairs should be zero except a few, but dense embeddings will lead to nonzero predictions for all feature pairs, and thus can overgeneralize. On the other hand, linear models with crossed features can memorize these “exception rules” effectively with fewer model parameters.
Now, let's see how to jointly train wide and deep models and allow them to complement each other’s strengths and weaknesses.
Combining Wide and Deep Models into One
The wide models and deep models are combined by summing up their final output
log odds as the prediction, then feeding the prediction to a logistic loss
function. All the graph definition and variable allocations have already been
handled for you under the hood, so you simply need to create a
DNNLinearCombinedClassifier
:
import tempfile
model_dir = tempfile.mkdtemp()
m = tf.estimator.DNNLinearCombinedClassifier(
model_dir=model_dir,
linear_feature_columns=crossed_columns,
dnn_feature_columns=deep_columns,
dnn_hidden_units=[100, 50])
Training and Evaluating The Model
Before we train the model, let's read in the Census dataset as we did in the TensorFlow Linear Model tutorial. The code for input data processing is provided here again for your convenience:
import pandas as pd
import urllib
# Define the column names for the data sets.
CSV_COLUMNS = [
"age", "workclass", "fnlwgt", "education", "education_num",
"marital_status", "occupation", "relationship", "race", "gender",
"capital_gain", "capital_loss", "hours_per_week", "native_country",
"income_bracket"
]
def maybe_download(train_data, test_data):
"""Maybe downloads training data and returns train and test file names."""
if train_data:
train_file_name = train_data
else:
train_file = tempfile.NamedTemporaryFile(delete=False)
urllib.request.urlretrieve(
"https://archive.ics.uci.edu/ml/machinelearningdatabases/adult/adult.data",
train_file.name) # pylint: disable=linetoolong
train_file_name = train_file.name
train_file.close()
print("Training data is downloaded to %s" % train_file_name)
if test_data:
test_file_name = test_data
else:
test_file = tempfile.NamedTemporaryFile(delete=False)
urllib.request.urlretrieve(
"https://archive.ics.uci.edu/ml/machinelearningdatabases/adult/adult.test",
test_file.name) # pylint: disable=linetoolong
test_file_name = test_file.name
test_file.close()
print("Test data is downloaded to %s"% test_file_name)
return train_file_name, test_file_name
def input_fn(data_file, num_epochs, shuffle):
"""Input builder function."""
df_data = pd.read_csv(
tf.gfile.Open(data_file),
names=CSV_COLUMNS,
skipinitialspace=True,
engine="python",
skiprows=1)
# remove NaN elements
df_data = df_data.dropna(how="any", axis=0)
labels = df_data["income_bracket"].apply(lambda x: ">50K" in x).astype(int)
return tf.estimator.inputs.pandas_input_fn(
x=df_data,
y=labels,
batch_size=100,
num_epochs=num_epochs,
shuffle=shuffle,
num_threads=5)
After reading in the data, you can train and evaluate the model:
# set num_epochs to None to get infinite stream of data.
m.train(
input_fn=input_fn(train_file_name, num_epochs=None, shuffle=True),
steps=train_steps)
# set steps to None to run evaluation until all data consumed.
results = m.evaluate(
input_fn=input_fn(test_file_name, num_epochs=1, shuffle=False),
steps=None)
print("model directory = %s" % model_dir)
for key in sorted(results):
print("%s: %s" % (key, results[key]))
The first line of the output should be something like accuracy: 0.84429705
. We
can see that the accuracy was improved from about 83.6% using a wideonly linear
model to about 84.4% using a Wide & Deep model. If you'd like to see a working
endtoend example, you can download our
example code.
Note that this tutorial is just a quick example on a small dataset to get you familiar with the API. Wide & Deep Learning will be even more powerful if you try it on a large dataset with many sparse feature columns that have a large number of possible feature values. Again, feel free to take a look at our research paper for more ideas about how to apply Wide & Deep Learning in realworld largescale machine learning problems.