Hybrid Population Monte Carlo (2412.19576v1)

Abstract: Importance sampling (IS) is a powerful Monte Carlo (MC) technique for approximating intractable integrals, for instance in Bayesian inference. The performance of IS relies heavily on the appropriate choice of the so-called proposal distribution. Adaptive IS (AIS) methods iteratively improve target estimates by adapting the proposal distribution. Recent AIS research focuses on enhancing proposal adaptation for high-dimensional problems, while addressing the challenge of multi-modal targets. In this paper, a new class of AIS methods is presented, utilizing a hybrid approach that incorporates weighted samples and proposal distributions to enhance performance. This approach belongs to the family of population Monte Carlo (PMC) algorithms, where a population of proposals is adapted to better approximate the target distribution. The proposed hybrid population Monte Carlo (HPMC) implements a novel two-step adaptation mechanism. In the first step, a hybrid method is used to generate the population of the preliminary proposal locations based on both weighted samples and location parameters. We use Hamiltonian Monte Carlo (HMC) to generate the preliminary proposal locations. HMC has a good exploratory behavior, especially in high dimension scenarios. In the second step, the novel cooperation algorithms are performing to find the final proposals for the next iteration. HPMC achieves a significant performance improvement in high-dimensional problems when compared to the state-of-the-art algorithms. We discuss the statistical properties of HPMC and show its high performance in two challenging benchmarks.