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.

翻译：马尔可夫链蒙特卡洛（MCMC）为隐马尔可夫模型的推断提供了一种可行方法，然而其计算负担往往过大，尤其受限于维数灾难——蒙特卡洛采样器在参数空间的不确定区域内随机进行小步长遍历。我们首次将目标函数的后验分布视为无限维欧氏空间中的样本映射，此空间中嵌入了确定性子流形，并提出一种新准则：通过最大化加权Riesz极化量，利用成对相互作用对可求长子流形进行离散化。我们研究了切比雪夫粒子的特性，并将其嵌入序贯MCMC——一种仅需少量评估即可实现高接受率的新型采样器。在使用合成数据的线性高斯状态空间模型和真实数据的非线性随机波动模型参数推断实验中，我们均取得了高性能。