Robust Mixtures in the Presence of Measurement Errors

Robust Mixtures in the Presence of Measurement Errors
Jianyong Sun - School of Computer Science and School of Physics and Astronomy, University of Birmingham, United Kingdom Ata Kaban - School of Computer Science, University of Birmingham, United Kingdom Somak Raychaudhury - School of Physics and Astronomy, University of Birmingham, United Kingdom
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 for detecting peculiar quasars from an astrophysical survey, given photometric measurements with errors.

Jianyong Sun - School of Computer Science and School of Physics and Astronomy, University of Birmingham, United Kingdom
Ata Kaban - School of Computer Science, University of Birmingham, United Kingdom
Somak Raychaudhury - School of Physics and Astronomy, University of Birmingham, United Kingdom

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 for detecting peculiar quasars from an astrophysical survey, given photometric measurements with errors.