Robust mixtures in the presence of measurement errors

TL;DR

This paper introduces a robust mixture model incorporating measurement error information for outlier detection in multivariate data, demonstrated on astrophysical survey data to identify peculiar quasars.

Contribution

It develops a tree-structured variational EM algorithm for inference in a mixture model that accounts for measurement errors, improving outlier detection accuracy.

Findings

Enhanced outlier detection with measurement error inclusion

Tree-structured variational EM outperforms factorial approximation

Successful application to astrophysical data for quasar detection

Abstract

We develop a mixture-based approach to robust density modeling and outlier detection for experimental multivariate data that includes measurement error information. Our model is designed to infer atypical measurements that are not due to errors, aiming to retrieve potentially interesting peculiar objects. Since exact inference is not possible in this model, we develop a tree-structured variational EM solution. This compares favorably against a fully factorial approximation scheme, approaching the accuracy of a Markov-Chain-EM, while maintaining computational simplicity. We demonstrate the benefits of including measurement errors in the model, in terms of improved outlier detection rates in varying measurement uncertainty conditions. We then use this approach in detecting peculiar quasars from an astrophysical survey, given photometric measurements with errors.