An adaptive population importance sampler

Monte Carlo (MC) methods are widely used in signal processing, machine learning and communications for statistical inference and stochastic optimization. A well-known class of MC methods is composed of importance sampling and its adaptive extensions (e.g., population Monte Carlo). In this work, we introduce an adaptive importance sampler using a population of proposal densities. The novel algorithm provides a global estimation of the variables of interest iteratively, using all the samples generated. The cloud of proposals is adapted by learning from a subset of previously generated samples, in such a way that local features of the target density can be better taken into account compared to single global adaptation procedures. Numerical results show the advantages of the proposed sampling scheme in terms of mean absolute error and robustness to initialization

Adaptive multiple importance sampling for Gaussian processes and its application in social signal processing

Social signal processing aims to automatically understand and interpret social signals (e.g. facial expressions and prosody) generated during human-human and human-machine interactions. Automatic interpretation of social signals involves two fundamentally important aspects: feature extraction and machine learning. So far, machine learning approaches applied to social signal processing have mainly focused on parametric approaches (e.g. linear regression) or non-parametric models such as support vector machine (SVM). However, these approaches fall short of taking into account any uncertainty as a result of model misspecification or lack interpretability for analyses of scenarios in social signal processing. Consequently, they are less able to understand and interpret human behaviours effectively. Gaussian processes (GPs), that have gained popularity in data analysis, offer a solution to these limitations through their attractive properties: being non-parametric enables them to flexibly model data and being probabilistic makes them capable of quantifying uncertainty. In addition, a proper parametrisation in the covariance function makes it possible to gain insights into the application under study. However, these appealing properties of GP models hinge on an accurate characterisation of the posterior distribution with respect to the covariance parameters. This is normally done by means of standard MCMC algorithms, which require repeated expensive calculations involving the marginal likelihood. Motivated by the desire to avoid the inefficiencies of MCMC algorithms rejecting a considerable number of expensive proposals, this thesis has developed an alternative inference framework based on adaptive multiple importance sampling (AMIS). In particular, this thesis studies the application of AMIS for Gaussian processes in the case of a Gaussian likelihood, and proposes a novel pseudo-marginal-based AMIS (PM-AMIS) algorithm for non-Gaussian likelihoods, where the marginal likelihood is unbiasedly estimated. Experiments on benchmark data sets show that the proposed framework outperforms the MCMC-based inference of GP covariance parameters in a wide range of scenarios. The PM-AMIS classifier - based on Gaussian processes with a newly designed group-automatic relevance determination (G-ARD) kernel - has been applied to predict whether a Flickr user is perceived to be above the median or not with respect to each of the Big-Five personality traits. The results show that, apart from the high prediction accuracies achieved (up to 79% depending on the trait), the parameters of the G-ARD kernel allow the identification of the groups of features that better account for the classification outcome and provide indications about cultural effects through their weight differences. Therefore, this demonstrates the value of the proposed non-parametric probabilistic framework for social signal processing. Feature extraction in signal processing is dominated by various methods based on short time Fourier transform (STFT). Recently, Hilbert spectral analysis (HSA), a new representation of signal which is fundamentally different from STFT has been proposed. This thesis is also the first attempt to investigate the extraction of features from this newly proposed HSA and its application in social signal processing. The experimental results reveal that, using features extracted from the Hilbert spectrum of voice data of female speakers, the prediction accuracy can be achieved by up to 81% when predicting their Big-Five personality traits, and hence show that HSA can work as an effective alternative to STFT for feature extraction in social signal processing

Adaptive Non-uniform Compressive Sampling for Time-varying Signals

In this paper, adaptive non-uniform compressive sampling (ANCS) of time-varying signals, which are sparse in a proper basis, is introduced. ANCS employs the measurements of previous time steps to distribute the sensing energy among coefficients more intelligently. To this aim, a Bayesian inference method is proposed that does not require any prior knowledge of importance levels of coefficients or sparsity of the signal. Our numerical simulations show that ANCS is able to achieve the desired non-uniform recovery of the signal. Moreover, if the signal is sparse in canonical basis, ANCS can reduce the number of required measurements significantly.Comment: 6 pages, 8 figures, Conference on Information Sciences and Systems (CISS 2017) Baltimore, Marylan

Group Importance Sampling for Particle Filtering and MCMC

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 involving a posterior distribution by means of weighted samples. In this work, we study the assignation of a single weighted sample which compresses the information contained in a population of weighted samples. Part of the theory that we present as Group Importance Sampling (GIS) has been employed implicitly in different works in the literature. The provided analysis yields several theoretical and practical consequences. For instance, we discuss the application of GIS into the Sequential Importance Resampling framework and show that Independent Multiple Try Metropolis schemes can be interpreted as a standard Metropolis-Hastings algorithm, following the GIS approach. We also introduce two novel Markov Chain Monte Carlo (MCMC) techniques based on GIS. The first one, named Group Metropolis Sampling method, produces a Markov chain of sets of weighted samples. All these sets are then employed for obtaining a unique global estimator. The second one is the Distributed Particle Metropolis-Hastings technique, where different parallel particle filters are jointly used to drive an MCMC algorithm. Different resampled trajectories are compared and then tested with a proper acceptance probability. The novel schemes are tested in different numerical experiments such as learning the hyperparameters of Gaussian Processes, two localization problems in a wireless sensor network (with synthetic and real data) and the tracking of vegetation parameters given satellite observations, where they are compared with several benchmark Monte Carlo techniques. Three illustrative Matlab demos are also provided.Comment: To appear in Digital Signal Processing. Related Matlab demos are provided at https://github.com/lukafree/GIS.gi

Efficient Sequential Monte-Carlo Samplers for Bayesian Inference

In many problems, complex non-Gaussian and/or nonlinear models are required to accurately describe a physical system of interest. In such cases, Monte Carlo algorithms are remarkably flexible and extremely powerful approaches to solve such inference problems. However, in the presence of a high-dimensional and/or multimodal posterior distribution, it is widely documented that standard Monte-Carlo techniques could lead to poor performance. In this paper, the study is focused on a Sequential Monte-Carlo (SMC) sampler framework, a more robust and efficient Monte Carlo algorithm. Although this approach presents many advantages over traditional Monte-Carlo methods, the potential of this emergent technique is however largely underexploited in signal processing. In this work, we aim at proposing some novel strategies that will improve the efficiency and facilitate practical implementation of the SMC sampler specifically for signal processing applications. Firstly, we propose an automatic and adaptive strategy that selects the sequence of distributions within the SMC sampler that minimizes the asymptotic variance of the estimator of the posterior normalization constant. This is critical for performing model selection in modelling applications in Bayesian signal processing. The second original contribution we present improves the global efficiency of the SMC sampler by introducing a novel correction mechanism that allows the use of the particles generated through all the iterations of the algorithm (instead of only particles from the last iteration). This is a significant contribution as it removes the need to discard a large portion of the samples obtained, as is standard in standard SMC methods. This will improve estimation performance in practical settings where computational budget is important to consider.Comment: arXiv admin note: text overlap with arXiv:1303.3123 by other author

Orthogonal parallel MCMC methods for sampling and optimization

Monte Carlo (MC) methods are widely used for Bayesian inference and optimization in statistics, signal processing and machine learning. A well-known class of MC methods are Markov Chain Monte Carlo (MCMC) algorithms. In order to foster better exploration of the state space, specially in high-dimensional applications, several schemes employing multiple parallel MCMC chains have been recently introduced. In this work, we describe a novel parallel interacting MCMC scheme, called {\it orthogonal MCMC} (O-MCMC), where a set of "vertical" parallel MCMC chains share information using some "horizontal" MCMC techniques working on the entire population of current states. More specifically, the vertical chains are led by random-walk proposals, whereas the horizontal MCMC techniques employ independent proposals, thus allowing an efficient combination of global exploration and local approximation. The interaction is contained in these horizontal iterations. Within the analysis of different implementations of O-MCMC, novel schemes in order to reduce the overall computational cost of parallel multiple try Metropolis (MTM) chains are also presented. Furthermore, a modified version of O-MCMC for optimization is provided by considering parallel simulated annealing (SA) algorithms. Numerical results show the advantages of the proposed sampling scheme in terms of efficiency in the estimation, as well as robustness in terms of independence with respect to initial values and the choice of the parameters

Fast estimation of false alarm probabilities of STAP detectors - the AMF

This paper describes an attempt to harness the power of adaptive importance sampling techniques for estimating false alarm probabilities of detectors that use space-time adaptive processing. Fast simulation using these techniques have been notably successful in the study of conventional constant false alarm rate radar detectors, and in several other applications. The principal task here is to examine the viability of using importance sampling methods for STAP detection. Though a modest beginning, the adaptive matched filter detection algorithm is analysed successfully using fast simulation. Of the two biasing methods considered, one is implemented and shown to yield excellent results. The important problem of detector threshold determination is also addressed, with matching outcome. The work reported here serves to pave the way to development of more advanced estimation techniques that can facilitate design of powerful and robust detection algorithms designed to counter hostile and heterogeneous clutter environments

Robust Covariance Adaptation in Adaptive Importance Sampling

Importance sampling (IS) is a Monte Carlo methodology that allows for approximation of a target distribution using weighted samples generated from another proposal distribution. Adaptive importance sampling (AIS) implements an iterative version of IS which adapts the parameters of the proposal distribution in order to improve estimation of the target. While the adaptation of the location (mean) of the proposals has been largely studied, an important challenge of AIS relates to the difficulty of adapting the scale parameter (covariance matrix). In the case of weight degeneracy, adapting the covariance matrix using the empirical covariance results in a singular matrix, which leads to poor performance in subsequent iterations of the algorithm. In this paper, we propose a novel scheme which exploits recent advances in the IS literature to prevent the so-called weight degeneracy. The method efficiently adapts the covariance matrix of a population of proposal distributions and achieves a significant performance improvement in high-dimensional scenarios. We validate the new method through computer simulations

Metropolis Sampling

Monte Carlo (MC) sampling methods are widely applied in Bayesian inference, system simulation and optimization problems. The Markov Chain Monte Carlo (MCMC) algorithms are a well-known class of MC methods which generate a Markov chain with the desired invariant distribution. In this document, we focus on the Metropolis-Hastings (MH) sampler, which can be considered as the atom of the MCMC techniques, introducing the basic notions and different properties. We describe in details all the elements involved in the MH algorithm and the most relevant variants. Several improvements and recent extensions proposed in the literature are also briefly discussed, providing a quick but exhaustive overview of the current Metropolis-based sampling's world.Comment: Wiley StatsRef-Statistics Reference Online, 201