# Variational Information Bottleneck for Unsupervised Clustering: Deep Gaussian Mixture Embedding

## TL;DR

This paper introduces an unsupervised clustering method that combines the Variational Information Bottleneck with Gaussian Mixture Models, leveraging neural networks and variational inference for effective data embedding.

## Contribution

It develops a novel unsupervised generative clustering framework integrating the Variational Information Bottleneck with Gaussian Mixture Models, including a new bound and inference algorithm.

## Key findings

- Demonstrates efficiency on real datasets
- Provides a new variational bound generalizing ELBO
- Uses neural networks for flexible encoding

## Abstract

In this paper, we develop an unsupervised generative clustering framework that combines the Variational Information Bottleneck and the Gaussian Mixture Model. Specifically, in our approach, we use the Variational Information Bottleneck method and model the latent space as a mixture of Gaussians. We derive a bound on the cost function of our model that generalizes the Evidence Lower Bound (ELBO) and provide a variational inference type algorithm that allows computing it. In the algorithm, the coders' mappings are parametrized using neural networks, and the bound is approximated by Monte Carlo sampling and optimized with stochastic gradient descent. Numerical results on real datasets are provided to support the efficiency of our method.