# Mixed Likelihood Variational Gaussian Processes

arXiv: https://arxiv.org/abs/2503.04138 · HTML: https://mlsanity.com/paper/2503.04138/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 40 references that are in the map.
- First posted on arXiv 6 Mar 2025.

## Builds on (most cited first, 13 of 13)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Learning to summarize from human feedback](https://mlsanity.com/paper/2009.01325/) (2020)
- [Variational Inference: A Review for Statisticians](https://mlsanity.com/paper/1601.00670/) (2016)
- [Gaussian Processes for Big Data](https://mlsanity.com/paper/1309.6835/) (2013)
- [Scalable Variational Gaussian Process Classification](https://mlsanity.com/paper/1411.2005/) (2014)
- [Practical heteroskedastic Gaussian process modeling for large simulation experiments](https://mlsanity.com/paper/1611.05902/) (2016)
- [Heterogeneous Multi-output Gaussian Process Prediction](https://mlsanity.com/paper/1805.07633/) (2018)
- [Preference-Based Learning for Exoskeleton Gait Optimization](https://mlsanity.com/paper/1909.12316/) (2019)
- [Look-Ahead Acquisition Functions for Bernoulli Level Set Estimation](https://mlsanity.com/paper/2203.09751/) (2022)
- [Mixed Likelihood Gaussian Process Latent Variable Model](https://mlsanity.com/paper/1811.07627/) (2018)
- [Perceptual Requirements for World-Locked Rendering in AR and VR](https://mlsanity.com/paper/2303.15666/) (2023)
- [Saccade-Contingent Rendering](https://mlsanity.com/paper/2401.16536/) (2024)
- [A Unifying Variational Framework for Gaussian Process Motion Planning](https://mlsanity.com/paper/2309.00854/) (2023)

## Built on by (most cited first, 2 of 2)

- [Knowledge Gradient for Preference Learning](https://mlsanity.com/paper/2601.22335/) (2026)
- [Elicitation-Augmented Bayesian Optimization](https://mlsanity.com/paper/2605.12079/) (2026)

## Abstract (arXiv)

Gaussian processes (GPs) are powerful models for human-in-the-loop experiments due to their flexibility and well-calibrated uncertainty. However, GPs modeling human responses typically ignore auxiliary information, including a priori domain expertise and non-task performance information like user confidence ratings. We propose mixed likelihood variational GPs to leverage auxiliary information, which combine multiple likelihoods in a single evidence lower bound to model multiple types of data. We demonstrate the benefits of mixing likelihoods in three real-world experiments with human participants. First, we use mixed likelihood training to impose prior knowledge constraints in GP classifiers, which accelerates active learning in a visual perception task where users are asked to identify geometric errors resulting from camera position errors in virtual reality. Second, we show that leveraging Likert scale confidence ratings by mixed likelihood training improves model fitting for haptic perception of surface roughness. Lastly, we show that Likert scale confidence ratings improve human preference learning in robot gait optimization. The modeling performance improvements found using our framework across this diverse set of applications illustrates the benefits of incorporating auxiliary information into active learning and preference learning by using mixed likelihoods to jointly model multiple inputs.