# Generalized Multi-Output Gaussian Process Censored Regression

arXiv: https://arxiv.org/abs/2009.04822 · HTML: https://mlsanity.com/paper/2009.04822/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Sep 2020.

## Built on by (most cited first, 7 of 7)

- [Predictive and Prescriptive Performance of Bike-Sharing Demand Forecasts for Inventory Management](https://mlsanity.com/paper/2108.00858/) (2021)
- [Mind the Gap: Modelling Difference Between Censored and Uncensored Electric Vehicle Charging Demand](https://mlsanity.com/paper/2301.06418/) (2023)
- [Federated Automatic Latent Variable Selection in Multi-output Gaussian Processes](https://mlsanity.com/paper/2407.16935/) (2024)
- [Multi-Output Robust and Conjugate Gaussian Processes](https://mlsanity.com/paper/2510.26401/) (2025)
- [Gaussian Process Latent Class Choice Models](https://mlsanity.com/paper/2101.12252/) (2021)
- [Diffusion-aware Censored Gaussian Processes for Demand Modelling](https://mlsanity.com/paper/2501.12354/) (2025)
- [Residual Correlation as a Diagnostic for Joint-Uncertainty Gains from GP Coregionalisation](https://mlsanity.com/paper/2609.30085/) (2026)

## Abstract (arXiv)

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.