2024/02/14 by James Odgers, Ruby Sedgwick, Odgers, James +8 · 1 voice
Computer Science · Mathematics · #FOS: Computer and information sciences #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #cs.LG #stat.ML
paper · pdf · doi:10.48550/arxiv.2402.09122
openalex publication_date 2024/02/14 · arxiv published 2024/02/14 · openalex created_date 2024/02/16 · arxiv updated 2025/03/19 · openalex updated_date 2026/07/28
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.