2020/09/10 by Daniele Gammelli, Gammelli, Daniele, Kasper Pryds Rolsted +5 · 1 citation
Computer Science · #Advanced Multi-Objective Optimization Algorithms #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Data Classification
paper · pdf · doi:10.48550/arxiv.2009.04822
openalex publication_date 2020/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
When modelling censored observations, 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.