Generalized multi-output Gaussian process censored regression. (September 2022)

• Record Type: Journal Article
• Authors: Gammelli, Daniele; Rolsted, Kasper Pryds; Pacino, Dario; Rodrigues, Filipe
• Is Part Of: Pattern recognition. Volume 129(2022)
• Publication Date: 2022-09
• Subjects: Censored data -- Gaussian processes -- Variational inference; Pattern perception -- Periodicals; Perception des structures -- Périodiques; Patroonherkenning; 006.4
• DOI: 10.1016/j.patcog.2022.108751
• Languages: English
• ISSNs: 0031-3203

Abstract

Highlights: Censored data as defining characteristic of numerous domains in science. Heteroscedastic Multi-Output Gaussian Process formulated for censored regression. Generalization of arbitrary likelihood functions enabled by devising a variational bound to the marginal log-likelihood. Experiments with synthetic and real-world data demonstrate solution approach. Abstract: When modelling censored observations (i.e. data in which the value of a measurement or observation is un-observable beyond a given threshold), a typical approach in current regression methods is to use a censored-Gaussian (i.e. Tobit) model to describe the conditional output distribution. In this paper, as in the case of missing data, we argue that exploiting correlations between multiple outputs can enable models to better address the bias introduced by censored data. To do so, we introduce a heteroscedastic multi-output Gaussian process model which combines the non-parametric flexibility of GPs with the ability to leverage information from correlated outputs under input-dependent noise conditions. To address the resulting inference intractability, we further devise a variational bound to the marginal log-likelihood suitable for stochastic optimization. We empirically evaluate our model against other generative models for censored data on both synthetic and real world tasks and further show how it can be generalized to deal with arbitrary likelihood functions. Results show how the added flexibility allows our model to better estimate the underlying non-censored (i.e. true) process under potentially complex censoring dynamics.