Scalable Importance Tempering and Bayesian Variable Selection
This work addresses scalability issues in Bayesian variable selection for researchers and practitioners dealing with high-dimensional data, representing a strong specific gain rather than a broad paradigm shift.
The authors tackled the problem of sampling from high-dimensional probability distributions by proposing a Monte Carlo algorithm that combines Markov chain Monte Carlo and importance sampling, resulting in orders of magnitude greater efficiency than alternative methods, enabling Bayesian inferences with tens of thousands of regressors.
We propose a Monte Carlo algorithm to sample from high dimensional probability distributions that combines Markov chain Monte Carlo and importance sampling. We provide a careful theoretical analysis, including guarantees on robustness to high dimensionality, explicit comparison with standard Markov chain Monte Carlo methods and illustrations of the potential improvements in efficiency. Simple and concrete intuition is provided for when the novel scheme is expected to outperform standard schemes. When applied to Bayesian variable-selection problems, the novel algorithm is orders of magnitude more efficient than available alternative sampling schemes and enables fast and reliable fully Bayesian inferences with tens of thousand regressors.