Multiple output samples per input in a single-output Gaussian process
Abstract
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.
Cite
@article{arxiv.2306.02719,
title = {Multiple output samples per input in a single-output Gaussian process},
author = {Jeremy H. M. Wong and Huayun Zhang and Nancy F. Chen},
journal= {arXiv preprint arXiv:2306.02719},
year = {2024}
}
Comments
This paper is presented in the "Symposium for Celebrating 40 Years of Bayesian Learning in Speech and Language Processing and Beyond", which is a satellite event of the ASRU workshop, on 20 December 2023. https://bayesian40.github.io/