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 feed-forward neural network. This approach combines the strengths of memorization and generalization. It's useful for generic large-scale 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 (feed-forward 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.

Execute the data download script we provide to you:

`$ python data_download.py`

Execute the tutorial code with the following command to train the wide and deep model described in this tutorial:

`$ python wide_deep.py`

Read on to find out how this code builds its 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
# Continuous 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')
education = tf.feature_column.categorical_column_with_vocabulary_list(
'education', [
'Bachelors', 'HS-grad', '11th', 'Masters', '9th', 'Some-college',
'Assoc-acdm', 'Assoc-voc', '7th-8th', 'Doctorate', 'Prof-school',
'5th-6th', '10th', '1st-4th', 'Preschool', '12th'])
marital_status = tf.feature_column.categorical_column_with_vocabulary_list(
'marital_status', [
'Married-civ-spouse', 'Divorced', 'Married-spouse-absent',
'Never-married', 'Separated', 'Married-AF-spouse', 'Widowed'])
relationship = tf.feature_column.categorical_column_with_vocabulary_list(
'relationship', [
'Husband', 'Not-in-family', 'Wife', 'Own-child', 'Unmarried',
'Other-relative'])
workclass = tf.feature_column.categorical_column_with_vocabulary_list(
'workclass', [
'Self-emp-not-inc', 'Private', 'State-gov', 'Federal-gov',
'Local-gov', '?', 'Self-emp-inc', 'Without-pay', 'Never-worked'])
# To show an example of hashing:
occupation = tf.feature_column.categorical_column_with_hash_bucket(
'occupation', hash_bucket_size=1000)
# 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 = [
education, marital_status, relationship, workclass, occupation,
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),
]
```

You can also see the TensorFlow Linear Model Tutorial for more details.

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 feed-forward neural network, as shown in the previous figure. Each of the sparse, high-dimensional categorical features are first converted into a low-dimensional and dense real-valued vector, often referred to as an embedding vector. These low-dimensional 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 one-hot or multi-hot representation. This is often appropriate for
categorical columns with only a few possible values. As an example of a one-hot
representation, for the relationship column, `"Husband"`

can be represented as
[1, 0, 0, 0, 0, 0], and `"Not-in-family"`

as [0, 1, 0, 0, 0, 0], etc. 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 multi-hot representations of some
categorical columns.

```
deep_columns = [
age,
education_num,
capital_gain,
capital_loss,
hours_per_week,
tf.feature_column.indicator_column(workclass),
tf.feature_column.indicator_column(education),
tf.feature_column.indicator_column(marital_status),
tf.feature_column.indicator_column(relationship),
# To show an example of embedding
tf.feature_column.embedding_column(occupation, dimension=8),
]
```

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 low-dimensional representations for feature columns when the underlying interaction matrix between two feature columns is sparse and high-rank. 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 over-generalize. 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`

:

```
model = tf.estimator.DNNLinearCombinedClassifier(
model_dir='/tmp/census_model',
linear_feature_columns=base_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. See `data_download.py`

as well as
`input_fn`

within
`wide_deep.py`

.

After reading in the data, you can train and evaluate the model:

```
# Train and evaluate the model every `FLAGS.epochs_per_eval` epochs.
for n in range(FLAGS.train_epochs // FLAGS.epochs_per_eval):
model.train(input_fn=lambda: input_fn(
FLAGS.train_data, FLAGS.epochs_per_eval, True, FLAGS.batch_size))
results = model.evaluate(input_fn=lambda: input_fn(
FLAGS.test_data, 1, False, FLAGS.batch_size))
# Display evaluation metrics
print('Results at epoch', (n + 1) * FLAGS.epochs_per_eval)
print('-' * 30)
for key in sorted(results):
print('%s: %s' % (key, results[key]))
```

The final output accuracy should be somewhere around 85.5%. If you'd like to see a working end-to-end 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 real-world large-scale machine learning problems.