Weighted Sum of Gaussian Process Latent Variable Models

James A C Odgers, Ruby Sedgwick, Chrysoula Dimitra Kappatou, Ruth Misener, Sarah Lucie Filippi
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3610-3618, 2025.

Abstract

This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) for the case where each data point comprises the weighted sum of a known number of pure component signals, observed across several input locations. Our framework allows arbitrary non-linear variations in the signals while being able to incorporate useful priors for the linear weights, such as summing-to-one. Our contributions are particularly relevant to spectroscopy, where changing conditions may cause the underlying pure component signals to vary from sample to sample. To demonstrate the applicability to both spectroscopy and other domains, we consider several applications: a near-infrared spectroscopy dataset with varying temperatures, a simulated dataset for identifying flow configuration through a pipe, and a dataset for determining the type of rock from its reflectance.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-odgers25a, title = {Weighted Sum of Gaussian Process Latent Variable Models}, author = {Odgers, James A C and Sedgwick, Ruby and Kappatou, Chrysoula Dimitra and Misener, Ruth and Filippi, Sarah Lucie}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3610--3618}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/odgers25a/odgers25a.pdf}, url = {https://proceedings.mlr.press/v258/odgers25a.html}, abstract = {This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) for the case where each data point comprises the weighted sum of a known number of pure component signals, observed across several input locations. Our framework allows arbitrary non-linear variations in the signals while being able to incorporate useful priors for the linear weights, such as summing-to-one. Our contributions are particularly relevant to spectroscopy, where changing conditions may cause the underlying pure component signals to vary from sample to sample. To demonstrate the applicability to both spectroscopy and other domains, we consider several applications: a near-infrared spectroscopy dataset with varying temperatures, a simulated dataset for identifying flow configuration through a pipe, and a dataset for determining the type of rock from its reflectance.} }
Endnote
%0 Conference Paper %T Weighted Sum of Gaussian Process Latent Variable Models %A James A C Odgers %A Ruby Sedgwick %A Chrysoula Dimitra Kappatou %A Ruth Misener %A Sarah Lucie Filippi %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-odgers25a %I PMLR %P 3610--3618 %U https://proceedings.mlr.press/v258/odgers25a.html %V 258 %X This work develops a Bayesian non-parametric approach to signal separation where the signals may vary according to latent variables. Our key contribution is to augment Gaussian Process Latent Variable Models (GPLVMs) for the case where each data point comprises the weighted sum of a known number of pure component signals, observed across several input locations. Our framework allows arbitrary non-linear variations in the signals while being able to incorporate useful priors for the linear weights, such as summing-to-one. Our contributions are particularly relevant to spectroscopy, where changing conditions may cause the underlying pure component signals to vary from sample to sample. To demonstrate the applicability to both spectroscopy and other domains, we consider several applications: a near-infrared spectroscopy dataset with varying temperatures, a simulated dataset for identifying flow configuration through a pipe, and a dataset for determining the type of rock from its reflectance.
APA
Odgers, J.A.C., Sedgwick, R., Kappatou, C.D., Misener, R. & Filippi, S.L.. (2025). Weighted Sum of Gaussian Process Latent Variable Models. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3610-3618 Available from https://proceedings.mlr.press/v258/odgers25a.html.

Related Material