InClass Nets: Independent Classifier Networks for Nonparametric Estimation of Conditional Independence Mixture Models and Unsupervised Classification

TL;DR

This paper introduces InClass nets, a neural network-based nonparametric method for estimating conditional independence mixture models, capable of handling high-dimensional variates and applicable to unsupervised classification tasks.

Contribution

The paper presents a novel neural network approach for nonparametric estimation of CIMMs, including new identifiability results and a practical Python implementation.

Findings

Successfully estimates CIMMs in high-dimensional settings

Provides new theoretical conditions for model identifiability

Validated with multiple examples and applications

Abstract

We introduce a new machine-learning-based approach, which we call the Independent Classifier networks (InClass nets) technique, for the nonparameteric estimation of conditional independence mixture models (CIMMs). We approach the estimation of a CIMM as a multi-class classification problem, since dividing the dataset into different categories naturally leads to the estimation of the mixture model. InClass nets consist of multiple independent classifier neural networks (NNs), each of which handles one of the variates of the CIMM. Fitting the CIMM to the data is performed by simultaneously training the individual NNs using suitable cost functions. The ability of NNs to approximate arbitrary functions makes our technique nonparametric. Further leveraging the power of NNs, we allow the conditionally independent variates of the model to be individually high-dimensional, which is the main advantage of our technique over existing non-machine-learning-based approaches. We derive some new results on the nonparametric identifiability of bivariate CIMMs, in the form of a necessary and a (different) sufficient condition for a bivariate CIMM to be identifiable. We provide a public implementation of InClass nets as a Python package called RainDancesVI and validate our InClass nets technique with several worked out examples. Our method also has applications in unsupervised and semi-supervised classification problems.