# Multiple output samples per input in a single-output Gaussian process

arXiv: https://arxiv.org/abs/2306.02719 · HTML: https://mlsanity.com/paper/2306.02719/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 27 references that are in the map.
- First posted on arXiv 5 Jun 2023.

## Builds on (most cited first, 6 of 6)

- [Efficient Estimation of Word Representations in Vector Space](https://mlsanity.com/paper/1301.3781/) (2013)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [The Promises and Pitfalls of Deep Kernel Learning](https://mlsanity.com/paper/2102.12108/) (2021)
- [speechocean762: An Open-Source Non-native English Speech Corpus For Pronunciation Assessment](https://mlsanity.com/paper/2104.01378/) (2021)
- [Multilingual Speech Evaluation: Case Studies on English, Malay and Tamil](https://mlsanity.com/paper/2107.03675/) (2021)

## Abstract (arXiv)

The standard Gaussian Process (GP) only considers a single output sample per input in the training set. Datasets for subjective tasks, such as spoken language assessment, may be annotated with output labels from multiple human raters per input. This paper proposes to generalise the GP to allow for these multiple output samples in the training set, and thus make use of available output uncertainty information. This differs from a multi-output GP, as all output samples are from the same task here. The output density function is formulated to be the joint likelihood of observing all output samples, and latent variables are not repeated to reduce computation cost. The test set predictions are inferred similarly to a standard GP, with a difference being in the optimised hyper-parameters. This is evaluated on speechocean762, showing that it allows the GP to compute a test set output distribution that is more similar to the collection of reference outputs from the multiple human raters.