Chebyshev Particles

TL;DR

This paper introduces Chebyshev particles, a novel sampling method that improves Markov chain Monte Carlo efficiency by embedding deterministic submanifolds and maximizing Riesz polarization, demonstrated on state-space and volatility models.

Contribution

It proposes a new Chebyshev particle approach that discretizes submanifolds and integrates into sequential MCMC, enhancing sampling efficiency and acceptance rates.

Findings

High acceptance ratio in sequential MCMC with Chebyshev particles

Effective parameter inference on Gaussian and stochastic volatility models

Superior performance over traditional methods in experiments

Abstract

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses randomly taking small steps within uncertain regions in the parameter space. We are the first to consider the posterior distribution of the objective as a mapping of samples in an infinite-dimensional Euclidean space where deterministic submanifolds are embedded and propose a new criterion by maximizing the weighted Riesz polarization quantity, to discretize rectifiable submanifolds via pairwise interaction. We study the characteristics of Chebyshev particles and embed them into sequential MCMC, a novel sampler with a high acceptance ratio that proposes only a few evaluations. We have achieved high performance from the experiments for parameter inference in a linear Gaussian state-space model with synthetic data and a non-linear stochastic volatility model with real-world data.