Mixed Naive Bayes

Naive Bayes classifiers are a set of supervised learning algorithms based on applying Bayes' theorem, but with strong independence assumptions between the features given the value of the class variable (hence naive).

This module implements categorical (multinoulli) and Gaussian naive Bayes algorithms (hence mixed naive Bayes). This means that we are not confined to the assumption that features (given their respective y's) follow the Gaussian distribution, but also the categorical distribution. Hence it is natural that the continuous data be attributed to the Gaussian and the categorical data (nominal or ordinal) be attributed the the categorical distribution.

The motivation for writing this library is that scikit-learn at the point of writing this (Sep 2019) did not have an implementation for mixed type of naive Bayes. They have one for CategoricalNB here but it's still in its infancy. scikit-learn now has CategoricalNB!

I like scikit-learn's APIs so if you use it a lot, you'll find that it's easy to get started started with this library. There's fit(), predict(), predict_proba() and score().

I've also written a tutorial here for naive bayes if you need to understand a bit more on the math.

Contents

• Installation
• Quick starts
• Benchmarks
• Tests
• API Documentation
• References
• Related work
• Contributing

Installation

via pip

bash pip install mixed-naive-bayes

or the nightly version

bash pip install git+https://github.com/remykarem/mixed-naive-bayes#egg=mixed-naive-bayes

Quick starts

Example 1: Discrete and continuous data

Below is an example of a dataset with discrete (first 2 columns) and continuous data (last 2). We assume that the discrete features follow a categorical distribution and the features with the continuous data follow a Gaussian distribution. Specify categorical_features=[0,1] then fit and predict as per usual.

python from mixed_naive_bayes import MixedNB X = [[0, 0, 180.9, 75.0], [1, 1, 165.2, 61.5], [2, 1, 166.3, 60.3], [1, 1, 173.0, 68.2], [0, 2, 178.4, 71.0]] y = [0, 0, 1, 1, 0] clf = MixedNB(categorical_features=[0,1]) clf.fit(X,y) clf.predict(X)

NOTE: The module expects that the categorical data be label-encoded accordingly. See the following example to see how.

Example 2: Discrete and continuous data

Below is a similar dataset. However, for this dataset we assume a categorical distribution on the first 3 features, and a Gaussian distribution on the last feature. Feature 3 however has not been label-encoded. We can use sklearn's LabelEncoder() preprocessing module to fix this.

```python import numpy as np from sklearn.preprocessing import LabelEncoder X = [[0, 0, 180, 75.0], [1, 1, 165, 61.5], [2, 1, 166, 60.3], [1, 1, 173, 68.2], [0, 2, 178, 71.0]] y = [0, 0, 1, 1, 0] X = np.array(X) y = np.array(y) labelencoder = LabelEncoder() X[:,2] = labelencoder.fit_transform(X[:,2]) print(X)

array([[ 0, 0, 4, 75],

[ 1, 1, 0, 61],

[ 2, 1, 1, 60],

[ 1, 1, 2, 68],

[ 0, 2, 3, 71]])

```

Then fit and predict as usual, specifying categorical_features=[0,1,2] as the indices that we assume categorical distribution.

python from mixed_naive_bayes import MixedNB clf = MixedNB(categorical_features=[0,1,2]) clf.fit(X,y) clf.predict(X)

Example 3: Discrete data only

If all columns are to be treated as discrete, specify categorical_features='all'.

python from mixed_naive_bayes import MixedNB X = [[0, 0], [1, 1], [1, 0], [0, 1], [1, 1]] y = [0, 0, 1, 0, 1] clf = MixedNB(categorical_features='all') clf.fit(X,y) clf.predict(X)

NOTE: The module expects that the categorical data be label-encoded accordingly. See the previous example to see how.

Example 4: Continuous data only

If all features are assumed to follow Gaussian distribution, then leave the constructor blank.

python from mixed_naive_bayes import MixedNB X = [[0, 0], [1, 1], [1, 0], [0, 1], [1, 1]] y = [0, 0, 1, 0, 1] clf = MixedNB() clf.fit(X,y) clf.predict(X)

More examples

See the examples/ folder for more example notebooks or jump into a notebook hosted at MyBinder here. Jupyter notebooks are generated using p2j.

Benchmarks

Performance across sklearn's datasets on classification tasks. Run python benchmarks.py.

Dataset | GaussianNB | MixedNB (G) | MixedNB (C) | MixedNB (C+G) | ------- | ---------- | ----------- | ----------- | ------------- | Iris plants | 0.960 | 0.960 | - | - | Handwritten digits | 0.858 | 0.858 | 0.961 | - | Wine | 0.989 | 0.989 | - | - | Breast cancer | 0.942 | 0.942 | - | - | Forest covertypes | 0.616 | 0.616 | - | 0.657 |

• GaussianNB - sklearn's API for Gaussian Naive Bayes
• MixedNB (G) - our API for Gaussian Naive Bayes
• MixedNB (C) - our API for Categorical Naive Bayes
• MixedNB (C+G) - our API for Naive Bayes where some features follow categorical distribution, and some features follow Gaussian

Tests

To run tests, pip install -r requirements-dev.txt

bash pytest

API Documentation

For more information on usage of the API, visit here. This was generated using pdoc3.

References

• scikit-learn's naive bayes

Related Work

• Categorical naive Bayes by scikit-learn
• Naive Bayes classifier for categorical and numerical data
• Generalised naive Bayes classifier

Contributing

Please submit your pull requests, will appreciate it a lot

If you use this software for your work, please cite us as follows:

@article{bin_Karim_Mixed_Naive_Bayes_2019, author = {bin Karim, Raimi}, journal = {https://github.com/remykarem/mixed-naive-bayes}, month = {10}, title = {{Mixed Naive Bayes}}, year = {2019} }