Generative, Fully Bayesian, Gaussian, Openset Pattern Classifier

TL;DR

This paper develops a fully Bayesian, Gaussian-based openset pattern classifier with closed-form solutions, enabling effective recognition of known and unknown classes using predictive likelihoods.

Contribution

It introduces a novel closed-form Bayesian multiclass classifier with a shared covariance structure and an evidence-based method for handling unseen classes.

Findings

Provides a closed-form expression for model evidence.

Enables recognition of unseen classes via predictive likelihoods.

Integrates all parameters in closed form for efficient computation.

Abstract

This report works out the details of a closed-form, fully Bayesian, multiclass, openset, generative pattern classifier using multivariate Gaussian likelihoods, with conjugate priors. The generative model has a common within-class covariance, which is proportional to the between-class covariance in the conjugate prior. The scalar proportionality constant is the only plugin parameter. All other model parameters are intergated out in closed form. An expression is given for the model evidence, which can be used to make plugin estimates for the proportionality constant. Pattern recognition is done via the predictive likeihoods of classes for which training data is available, as well as a predicitve likelihood for any as yet unseen class.