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mixed-naive-bayes

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Naive Bayes with support for categorical and continuous data

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# 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](https://scikit-learn.org/) at the point of writing this (Sep 2019) did not have an implementation for mixed type of naive Bayes. <s>They have one for `CategoricalNB` [here](https://github.com/scikit-learn/scikit-learn/blob/86aea9915/sklearn/naive_bayes.py#L1021) but it's still in its infancy.</s> scikit-learn now has [CategoricalNB](https://scikit-learn.org/stable/modules/generated/sklearn.naive_bayes.CategoricalNB.html)!

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](https://remykarem.github.io/blog/naive-bayes) for naive bayes if you need to understand a bit more on the math.

## Contents

- [Installation](#installation)
- [Quick starts](#quick-starts)
- [Benchmarks](#benchmarks)
- [Tests](#tests)
- [API Documentation](#api-documentation)
- [References](#references)
- [Related work](#related-work)
- [Contributing ❤️](#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()`](https://scikit-learn.org/stable/modules/generated/sklearn.preprocessing.LabelEncoder.html) 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)
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.

```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](https://mybinder.org/v2/gh/remykarem/mixed-naive-bayes/master?filepath=%2Fexamples%2Fdataset_digits.ipynb). Jupyter notebooks are generated using [`p2j`](https://github.com/remykarem/python2jupyter).

## Benchmarks

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

Dataset | GaussianNB | MixedNB (G) | MixedNB (C) | MixedNB (C+G) |
------- | ---------- | ----------- | ----------- | ------------- |
[Iris plants](https://scikit-learn.org/stable/datasets/toy_dataset.html#iris-plants-dataset)    | 0.960      | 0.960       | -           | - |
[Handwritten digits](https://scikit-learn.org/stable/datasets/toy_dataset.html#optical-recognition-of-handwritten-digits-dataset)  | 0.858      | 0.858       | **0.961**   | - |
[Wine](https://scikit-learn.org/stable/datasets/toy_dataset.html#wine-recognition-dataset)    | 0.989      | 0.989       | -           | - |
[Breast cancer](https://scikit-learn.org/stable/datasets/toy_dataset.html#breast-cancer-wisconsin-diagnostic-dataset)  | 0.942      | 0.942       | -           | - |
[Forest covertypes](https://scikit-learn.org/stable/datasets/real_world.html#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](https://mixed-naive-bayes.readthedocs.io). This was generated using pdoc3.

## References

- [scikit-learn's naive bayes](https://scikit-learn.org/stable/modules/classes.html#module-sklearn.naive_bayes)

## Related Work

- [Categorical naive Bayes by scikit-learn](https://scikit-learn.org/dev/modules/generated/sklearn.naive_bayes.CategoricalNB.html)
- [Naive Bayes classifier for categorical and numerical data](https://github.com/wookieJ/naive-bayes)
- [Generalised naive Bayes classifier](https://github.com/ashkonf/HybridNaiveBayes)

## 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}
}
```

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