Weighted-Sum of Gaussian Process Latent Variable Models

2024-02-14

AI Summary

This work addresses the problem of nonlinear blind source separation under latent-variable-driven mixing. We propose a Bayesian nonparametric framework that extends the Gaussian Process Latent Variable Model (GPLVM) to weighted linear mixture observations—its first application to such settings. The method explicitly models joint latent dynamics modulating both pure component signals and their mixing weights, incorporating custom-designed kernel functions enforcing physical constraints (e.g., weight simplex). It supports nonlinear signal evolution and enables incorporation of domain-specific structural priors, making it suitable for real-world spectroscopic applications with varying experimental conditions. Evaluated on three tasks—temperature-responsive near-infrared spectroscopy, gas–liquid two-phase flow pattern identification, and rock reflectance classification—the approach achieves high-accuracy source signal demixing and interpretable latent state reconstruction, significantly improving both accuracy and interpretability in inverse modeling of complex mixing systems.

Technology Category

• Machine Learning: Bayesian Learning
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Relational Probabilistic Models

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

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.

Problem

• Develops Bayesian non-parametric signal separation method
• Augments GPLVMs for weighted sum of component signals
• Applies to spectroscopy and other domains with varying conditions

Innovation

• Bayesian non-parametric signal separation approach
• Augmented Gaussian Process Latent Variable Models
• Handles non-linear signal variations with priors