Chebyshev Particles
This addresses the curse of dimensionality in MCMC for practitioners in statistics and machine learning, though it appears incremental as it builds on existing MCMC methods.
The paper tackles the computational inefficiency of MCMC for Hidden Markov models by proposing Chebyshev particles embedded in a sequential MCMC sampler, achieving high performance with a high acceptance ratio and few evaluations in experiments on linear Gaussian and non-linear stochastic volatility models.
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.