Subset weighted-Tempered Gibbs Sampler (wTGS) has been recently introduced by Jankowiak to reduce the computation complexity per MCMC iteration in high-dimensional applications where the exact calculation of the posterior inclusion probabilities (PIP) is not essential. However, the Rao-Backwellized estimator associated with this sampler has a high variance as the ratio between the signal dimension and the number of conditional PIP estimations is large. In this paper, we design a new subset weighted-Tempered Gibbs Sampler (wTGS) where the expected number of computations of conditional PIPs per MCMC iteration can be much smaller than the signal dimension. Different from the subset wTGS and wTGS, our sampler has a variable complexity per MCMC iteration. We provide an upper bound on the variance of an associated Rao-Blackwellized estimator for this sampler at a finite number of iterations, $T$, and show that the variance is $O\big(\big(\frac{P}{S}\big)^2 \frac{\log T}{T}\big)$ for a given dataset where $S$ is the expected number of conditional PIP computations per MCMC iteration. Experiments show that our Rao-Blackwellized estimator can have a smaller variance than its counterpart associated with the subset wTGS.

翻译：子集加权退火吉布斯采样器（wTGS）近期由Jankowiak提出，旨在高维应用中降低每次MCMC迭代的计算复杂度，这些场景中无需精确计算后验包含概率（PIP）。然而，当信号维度与条件PIP估计次数之比很大时，与该采样器关联的Rao-Blackwellized估计器具有高方差。本文设计了一种新的子集加权退火吉布斯采样器（wTGS），其中每次MCMC迭代中条件PIP的期望计算次数可远小于信号维度。与子集wTGS和wTGS不同，我们的采样器每次迭代具有可变复杂度。我们为该采样器在有限迭代次数$T$下关联的Rao-Blackwellized估计器方差提供了上界，并证明对于给定数据集，方差为$O\big(\big(\frac{P}{S}\big)^2 \frac{\log T}{T}\big)$，其中$S$是每次MCMC迭代中条件PIP计算的期望次数。实验表明，我们的Rao-Blackwellized估计器可具有比子集wTGS对应估计器更小的方差。