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LinearRegression package

Bayesian linear regression model with conjugate normal-inverse-gamma prior.

License

This package is open source software.

It is licensed under the Apache License, Version 2.0 (the "License"); you may not use it except in compliance with the License. You may obtain a copy of the License at http://www.apache.org/licenses/LICENSE-2.0.

Getting started

To build, use:

birch build

To run, use:

birch sample --config config/linear_regression.json

Details

The model is given by:

\begin{align} \sigma^2 &\sim \mathrm{Inv\text{-}Gamma}(3, 4/10) \\ \boldsymbol{\beta} &\sim \mathcal{N}(0, I\sigma^2) \\ y_n &\sim \mathcal{N}(\mathbf{x}_n^{\top}\boldsymbol{\beta}, \sigma^2) \end{align}

The parameters are the noise variance \sigma^2 and vector of coefficients \boldsymbol{\beta}. The data consists of observations y_n and explanatory variables \mathbf{x}_n for n=1,\ldots,N.

Acknowledgements

This package contains a bike sharing data set from the Capital Bikeshare system in Washington D.C., studied in Fanaee-T and Gama (2014), and prepared in JSON format for Birch.

References

  1. H. Fanaee-T and J. Gama (2014). Event labeling combining ensemble detectors and background knowledge. Progress in Artificial Intelligence. 2:113-127.