Generalized multi-output Gaussian process censored regression

Daniele Gammelli*, Kasper Pryds Rolsted, Dario Pacino, Filipe Rodrigues

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


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.

Original languageEnglish
Article number108751
JournalPattern Recognition
Publication statusPublished - 2022


  • Censored data
  • Gaussian processes
  • Variational inference


Dive into the research topics of 'Generalized multi-output Gaussian process censored regression'. Together they form a unique fingerprint.

Cite this