Variational Tobit Gaussian Process Regression

Marno Basson, Tobias Louw, Theresa Smith

Research output: Contribution to journalArticlepeer-review

2 Citations (SciVal)


We propose a variational inference-based framework for training a Gaussian process regression model subject to censored observational data. Data censoring is a typical problem encountered during the data gathering procedure and requires specialized techniques to perform inference since the resulting probabilistic models are typically analytically intractable. In this article we exploit the variational sparse Gaussian process inducing variable framework and local variational methods to compute an analytically tractable lower bound on the true log marginal likelihood of the probabilistic model which can be used to perform Bayesian model training and inference. We demonstrate the proposed framework on synthetically-produced, noise-corrupted observational data, as well as on a real-world data set, subject to artificial censoring. The resulting predictions are comparable to existing methods to account for data censoring, but provides a significant reduction in computational cost.

Original languageEnglish
Article number64
Number of pages26
JournalStatistics and Computing
Issue number3
Publication statusPublished - 31 Mar 2023

Bibliographical note

Open access funding provided by Stellenbosch University. This work was supported in part by the Engineering and Physical Sciences Research Council (EPSRC) (EP/P028403/1) and the School of Data Science and Computational Thinking (Stellenbosch University).

Data Availability
No novel data was produced during this study. The electrical conductivity (EC) data set, for the Vaal River at Groot Vadersbosch/Buffelsfontein, was obtained from the Department of Water and Sanitation, South Africa.


  • Bayesian statistics
  • Censored data
  • Gaussian process regression
  • Local variational methods
  • Tobit regression
  • Variational inference

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Computational Theory and Mathematics


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