# TensorFlow Wide & Deep Learning Tutorial

In the previous @{$wide$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](https://archive.ics.uci.edu/ml/datasets/Census+Income).
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.Learn 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](http://arxiv.org/abs/1606.07792).

![Wide & Deep Spectrum of Models]
(../images/wide_n_deep.svg "Wide & Deep")

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.Learn API:

1.  Select features for the wide part: Choose the sparse base columns and
    crossed columns you want to use.
1.  Select features for the deep part: Choose the continuous columns, the
    embedding dimension for each categorical column, and the hidden layer sizes.
1.  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:

1.  @{$install$Install TensorFlow} if you haven't already.

2.  Download [the tutorial code](https://www.tensorflow.org/code/tensorflow/examples/learn/wide_n_deep_tutorial.py).

3.  Install the pandas data analysis library. tf.learn doesn't require pandas, but it does support it, and this tutorial uses pandas. To install pandas:
    1. Get `pip`:

       ```bsh
       # Ubuntu/Linux 64-bit
       $ sudo apt-get install python-pip python-dev

       # Mac OS X
       $ sudo easy_install pip
       $ sudo easy_install --upgrade six
      ```

    2. Use `pip` to install pandas:

       ```bsh
       $ sudo pip install pandas
       ```

    If you have trouble installing pandas, consult the
    [instructions](http://pandas.pydata.org/pandas-docs/stable/install.html)
    on the pandas site.

4. Execute the tutorial code with the following command to train the linear
model described in this tutorial:

   ```shell
   $ 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.

```python
import tensorflow as tf

# Categorical base columns.
gender = tf.contrib.layers.sparse_column_with_keys(column_name="gender", keys=["Female", "Male"])
race = tf.contrib.layers.sparse_column_with_keys(column_name="race", keys=[
  "Amer-Indian-Eskimo", "Asian-Pac-Islander", "Black", "Other", "White"])
education = tf.contrib.layers.sparse_column_with_hash_bucket("education", hash_bucket_size=1000)
relationship = tf.contrib.layers.sparse_column_with_hash_bucket("relationship", hash_bucket_size=100)
workclass = tf.contrib.layers.sparse_column_with_hash_bucket("workclass", hash_bucket_size=100)
occupation = tf.contrib.layers.sparse_column_with_hash_bucket("occupation", hash_bucket_size=1000)
native_country = tf.contrib.layers.sparse_column_with_hash_bucket("native_country", hash_bucket_size=1000)

# Continuous base columns.
age = tf.contrib.layers.real_valued_column("age")
age_buckets = tf.contrib.layers.bucketized_column(age, boundaries=[18, 25, 30, 35, 40, 45, 50, 55, 60, 65])
education_num = tf.contrib.layers.real_valued_column("education_num")
capital_gain = tf.contrib.layers.real_valued_column("capital_gain")
capital_loss = tf.contrib.layers.real_valued_column("capital_loss")
hours_per_week = tf.contrib.layers.real_valued_column("hours_per_week")
```

## 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:

```python
wide_columns = [
  gender, native_country, education, occupation, workclass, relationship, age_buckets,
  tf.contrib.layers.crossed_column([education, occupation], hash_bucket_size=int(1e4)),
  tf.contrib.layers.crossed_column([native_country, occupation], hash_bucket_size=int(1e4)),
  tf.contrib.layers.crossed_column([age_buckets, education, occupation], hash_bucket_size=int(1e6))]
```

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](https://www.tensorflow.org/versions/r0.9/tutorials/word2vec/index.html),
or [Word Embedding](https://en.wikipedia.org/wiki/Word_embedding) on Wikipedia.

We'll configure the embeddings for the categorical columns using
`embedding_column`, and concatenate them with the continuous columns:

```python
deep_columns = [
  tf.contrib.layers.embedding_column(workclass, dimension=8),
  tf.contrib.layers.embedding_column(education, dimension=8),
  tf.contrib.layers.embedding_column(gender, dimension=8),
  tf.contrib.layers.embedding_column(relationship, dimension=8),
  tf.contrib.layers.embedding_column(native_country, dimension=8),
  tf.contrib.layers.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 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`:

```python
import tempfile
model_dir = tempfile.mkdtemp()
m = tf.contrib.learn.DNNLinearCombinedClassifier(
    model_dir=model_dir,
    linear_feature_columns=wide_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
@{$wide$TensorFlow Linear Model tutorial}. The code for
input data processing is provided here again for your convenience:

```python
import pandas as pd
import urllib

# Define the column names for the data sets.
COLUMNS = ["age", "workclass", "fnlwgt", "education", "education_num",
  "marital_status", "occupation", "relationship", "race", "gender",
  "capital_gain", "capital_loss", "hours_per_week", "native_country", "income_bracket"]
LABEL_COLUMN = 'label'
CATEGORICAL_COLUMNS = ["workclass", "education", "marital_status", "occupation",
                       "relationship", "race", "gender", "native_country"]
CONTINUOUS_COLUMNS = ["age", "education_num", "capital_gain", "capital_loss",
                      "hours_per_week"]

# Download the training and test data to temporary files.
# Alternatively, you can download them yourself and change train_file and
# test_file to your own paths.
train_file = tempfile.NamedTemporaryFile()
test_file = tempfile.NamedTemporaryFile()
urllib.urlretrieve("http://mlr.cs.umass.edu/ml/machine-learning-databases/adult/adult.data", train_file.name)
urllib.urlretrieve("http://mlr.cs.umass.edu/ml/machine-learning-databases/adult/adult.test", test_file.name)

# Read the training and test data sets into Pandas dataframe.
df_train = pd.read_csv(train_file, names=COLUMNS, skipinitialspace=True)
df_test = pd.read_csv(test_file, names=COLUMNS, skipinitialspace=True, skiprows=1)
df_train[LABEL_COLUMN] = (df_train['income_bracket'].apply(lambda x: '>50K' in x)).astype(int)
df_test[LABEL_COLUMN] = (df_test['income_bracket'].apply(lambda x: '>50K' in x)).astype(int)

def input_fn(df):
  # Creates a dictionary mapping from each continuous feature column name (k) to
  # the values of that column stored in a constant Tensor.
  continuous_cols = {k: tf.constant(df[k].values)
                     for k in CONTINUOUS_COLUMNS}
  # Creates a dictionary mapping from each categorical feature column name (k)
  # to the values of that column stored in a tf.SparseTensor.
  categorical_cols = {k: tf.SparseTensor(
      indices=[[i, 0] for i in range(df[k].size)],
      values=df[k].values,
      dense_shape=[df[k].size, 1])
                      for k in CATEGORICAL_COLUMNS}
  # Merges the two dictionaries into one.
  feature_cols = dict(continuous_cols.items() + categorical_cols.items())
  # Converts the label column into a constant Tensor.
  label = tf.constant(df[LABEL_COLUMN].values)
  # Returns the feature columns and the label.
  return feature_cols, label

def train_input_fn():
  return input_fn(df_train)

def eval_input_fn():
  return input_fn(df_test)
```

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

```python
m.fit(input_fn=train_input_fn, steps=200)
results = m.evaluate(input_fn=eval_input_fn, steps=1)
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 wide-only linear
model to about 84.4% using a Wide & Deep model. If you'd like to see a working
end-to-end example, you can download our
[example code](https://www.tensorflow.org/code/tensorflow/examples/learn/wide_n_deep_tutorial.py).

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](http://arxiv.org/abs/1606.07792) for more ideas about how to
apply Wide & Deep Learning in real-world large-scale machine learning problems.
