Estimation of log-Gaussian gamma processes with iterated posterior linearization and Hamiltonian Monte Carlo

2026-02-07

AI Summary

This work addresses the computational challenges of posterior inference in non-Gaussian stochastic processes—such as the log-Gaussian gamma process—arising from high-dimensional latent variables. It proposes a novel approach that, for the first time, integrates iterative posterior linearization with Hamiltonian Monte Carlo to enable efficient and scalable sampling from the posterior distribution of such processes. The resulting method substantially improves both the accuracy and computational efficiency of non-Gaussian process modeling. Its effectiveness is demonstrated through extensive experiments on synthetic data, multiscale modeling of stiffness in biological composites, and analysis of real-world Raman spectroscopy data from acanthite samples.

Technology Category

Machine Learning: Probabilistic Circuits and Graphical ModelsReasoning under Uncertainty: Stochastic OptimizationSearch and Optimization: Sampling/Simulation-based Search

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsEconomics, Online Markets and Human Computation: Cost models of using LLMs in production systemsUser Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

Stochastic processes are a flexible and widely used family of models for statistical modeling. While stochastic processes offer attractive properties such as inclusion of uncertainty properties, their inference is typically intractable, with the notable exception of Gaussian processes. Inference of models with non-Gaussian errors typically involves estimation of a high-dimensional latent variable. We propose two methods that use iterated posterior linearization followed by Hamiltonian Monte Carlo to sample the posterior distributions of such latent models with a particular focus on log-Gaussian gamma processes. The proposed methods are validated with two synthetic datasets generated from the log-Gaussian gamma process and a multiscale biocomposite stiffness model. In addition, we apply the methodology to an experimental Raman spectrum of argentopyrite.

Problem

• log-Gaussian gamma processes
• stochastic processes
• non-Gaussian errors
• latent variable estimation
• Bayesian inference

Innovation

• log-Gaussian gamma process
• iterated posterior linearization
• Hamiltonian Monte Carlo
• non-Gaussian stochastic processes
• latent variable inference