A comparison plot for sparse Bayesian regression with a half-cauchy prior (L), support vector regression (C), and the relevance vector machine (R). We see the half-cauchy prior provides a more sparse solution and better error bars.

What is VariationalSparseBayes?

This package provides an implementation of the algorithm described in Louizos et. al. (2017) for use on a broad class of machine learning problems.

Installation

pip install variationalsparsebayes

Usage

The library provides a high-level interface with some prebuilt sparse Bayesian models and a low-level interface for building custom sparse Bayesian models.

High-level interface

The library provides a few sparse Bayesian models:

• sparse polynomial regression
• sparse Bayesian neural networks.
• sparse learning with precomputed features

To implement your own linear model, you can inherit from the SparseFeaturesLibrary class. Note that I haven't implemented the "group" sparsity idea presented in Louizos et. al. (2017). Sparsification is performed at the parameter level (meaning far less computational savings).

Low-level interface

The most important class provided by the library is the SVIHalfCauchyPrior. The class inherits from nn.Module. The user is responsible for (i) transforming a batch of weights from the variational posterior into a batch of predictions and (ii) adding the KL-divergence provided by the prior onto the negative ELBO.

from torch import nn
from variationalsparsebayes import SVIHalfCauchyPrior

class MyModel(nn.Module):
    def __init__(self, num_params: int):
        super().__init__()
        # we initialize the prior with tau=1e-5 (see https://arxiv.org/pdf/1705.08665.pdf)
        self.prior = SVIHalfCauchyPrior(num_params, 1e-5)
        ...

    def forward(self, x, num_reparam_samples):
        w_samples = self.prior.get_reparam_weights(num_reparam_samples)
        sparse_index = self.prior.sparse_index
        # user transforms weights and inputs into predictions
        ...

    def elbo(self, x, y):
        return log_like(x, y) - self.prior.kl_divergence()

model = MyModel(num_params)
...

When it comes time to sparsify the approximate posterior run:

model.prior.update_sparse_index()
# get the index of all weights which remain after sparsification
model.prior.sparse_index