Variable Complexity Weighted-Tempered Gibbs Samplers for Bayesian Variable Selection
Abstract: A subset weighted-tempered Gibbs Sampler (subset-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 very high variance as the ratio between the signal dimension, $P$, and the number of conditional PIP estimations is large. In this paper, we design a new subset-wTGS where the expected number of computations of conditional PIPs per MCMC iteration can be much smaller than $P$. 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 any given dataset where $S$ is the expected number of conditional PIP computations per MCMC iteration.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Matthew_J._Holland1
Submission Number: 2205
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