Unsupervised Bayesian classification for models with scalar and functional covariates

TL;DR

This paper introduces a Bayesian unsupervised classification method for models with scalar and functional covariates, using basis expansion and variational inference to improve over traditional high-dimensional approaches.

Contribution

It proposes a hierarchical Bayesian model that effectively incorporates functional covariates via basis expansion and compares inference methods including Gibbs sampling and Variational Bayes.

Findings

The approach performs well in simulation studies with normal and zero-inflated Poisson mixtures.

Variational Bayes inference offers computational advantages over Gibbs sampling.

Dimensionality reduction via basis expansion improves model performance.

Abstract

We consider unsupervised classification by means of a latent multinomial variable which categorizes a scalar response into one of L components of a mixture model. This process can be thought as a hierarchical model with first level modelling a scalar response according to a mixture of parametric distributions, the second level models the mixture probabilities by means of a generalised linear model with functional and scalar covariates. The traditional approach of treating functional covariates as vectors not only suffers from the curse of dimensionality since functional covariates can be measured at very small intervals leading to a highly parametrised model but also does not take into account the nature of the data. We use basis expansion to reduce the dimensionality and a Bayesian approach to estimate the parameters while providing predictions of the latent classification vector. By means of a simulation study we investigate the behaviour of our approach considering normal mixture model and zero inflated mixture of Poisson distributions. We also compare the performance of the classical Gibbs sampling approach with Variational Bayes Inference.