ﻻ يوجد ملخص باللغة العربية
Bayesian models have become very popular over the last years in several fields such as signal processing, statistics, and machine learning. Bayesian inference requires the approximation of complicated integrals involving posterior distributions. For this purpose, Monte Carlo (MC) methods, such as Markov Chain Monte Carlo and importance sampling algorithms, are often employed. In this work, we introduce the theory and practice of a Compressed MC (C-MC) scheme to compress the statistical information contained in a set of random samples. In its basic version, C-MC is strictly related to the stratification technique, a well-known method used for variance reduction purposes. Deterministic C-MC schemes are also presented, which provide very good performance. The compression problem is strictly related to the moment matching approach applied in different filtering techniques, usually called as Gaussian quadrature rules or sigma-point methods. C-MC can be employed in a distributed Bayesian inference framework when cheap and fast communications with a central processor are required. Furthermore, C-MC is useful within particle filtering and adaptive IS algorithms, as shown by three novel schemes introduced in this work. Six numerical results confirm the benefits of the introduced schemes, outperforming the corresponding benchmark methods. A related code is also provided.
Bayesian methods and their implementations by means of sophisticated Monte Carlo techniques have become very popular in signal processing over the last years. Importance Sampling (IS) is a well-known Monte Carlo technique that approximates integrals
We introduce interacting particle Markov chain Monte Carlo (iPMCMC), a PMCMC method based on an interacting pool of standard and conditional sequential Monte Carlo samplers. Like related methods, iPMCMC is a Markov chain Monte Carlo sampler on an ext
Many problems in machine learning and statistics involve nested expectations and thus do not permit conventional Monte Carlo (MC) estimation. For such problems, one must nest estimators, such that terms in an outer estimator themselves involve calcul
We explore the construction of new symplectic numerical integration schemes to be used in Hamiltonian Monte Carlo and study their efficiency. Two integration schemes from Blanes et al. (2014), and a new scheme based on optimal acceptance probability,
There is an increasing interest in estimating expectations outside of the classical inference framework, such as for models expressed as probabilistic programs. Many of these contexts call for some form of nested inference to be applied. In this pape