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
• Requirements
• Performance (Accuracy)
• Performance (Speed)
• Tests
• API Documentation
• To-Dos
• References
• Related work
• Contributing ❤️

Installation

via pip

pip install mixed-naive-bayes

or

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.

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.

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)
label_encoder = LabelEncoder()
X[:,2] = label_encoder.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.

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'.

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.

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.

Requirements

• Python>=3.6
• numpy>=1.16.1
• scikit-learn>=0.20.2

The scikit-learn library is used to only import data as seen in the examples. Otherwise, the module itself does not require it.

The pytest library is not needed unless you want to perform testing.

Performance (Accuracy)

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

Performance (Speed)

The library is written in NumPy, so many operations are vectorised and faster than their for-loop counterparts. Fun fact: my first prototype (with many for-loops) took me 8 times slower than sklearn's 😱.

(Still measuring)

Tests

I'm still writing more test cases, but in the meantime, you can run the following:

pytest

• Correctness
• Accuracy against existing library (sklearn)
• Input type checking
• Example inputs

API Documentation

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

To-Dos

• Performance comparison
• Change to F-contiguous arrays?
• Implement predict_log_proba()
• Write more test cases
• Support refitting
• Regulariser for categorical distribution
• Variance smoothing for Gaussian distribution
• Vectorised main operations using NumPy

Possible features:

• Masking in NumPy
• Support label encoding

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 ❤