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.

本文提出了一种无监督的生成性聚类框架，将变分信息瓶颈和高斯混合模型相结合。使用变分信息瓶颈方法将潜空间建模为高斯混合物，并导出了一个代价函数的界限，并提供了一种可计算它的变分推断类型算法。通过神经网络参数化编码器映射，并通过蒙特卡罗采样逼近边界，并用随机梯度下降进行优化。提供了真实数据集的数值结果，证明了我们方法的有效性。