Adaptive Importance Sampling Algorithm Research Articles

A distributed particle filter with sampling-based consensus density fusion for speaker tracking in distributed microphone networks

This paper proposes a novel distributed particle filter with sampling-based consensus density fusion for speaker tracking in distributed microphone networks (DMNs). Firstly, to combat the reverberation and ambient noise, multi-hypothesis likelihood model is applied to describe the likelihood distribution in the state-space model of speaker tracking problem. Then, the sequential importance resampling (SIR) is performed on each node to obtain the local posteriors of the state vector of the speaker. Since the non-Gaussian noise and the reverberation may make local posteriors presenting non-Gaussian and multi-modal characters, in this paper, the local posterior densities are approximated by Gaussian mixtures whose parameters are further transmitted to neighboring nodes to complete the distributed fusion based on the consensus method. We investigate a novel adaptive multiple importance sampling (AMIS) algorithm combining parallel tempering Monte Carlo (PTMC) samplers to achieve the sampling-based consensus density fusion of the non-Gaussian local posteriors and estimate the global posterior locally on each node. At last, the optimal global estimation of the speaker state vector could be calculated by using the estimated global posterior on each node in DMNs. Simulation and real-world recording experiment results show that the proposed speaker tracking method exhibits satisfactory tracking performance under reverberant and noisy environments. Moreover, it is easy and feasible to extend the proposed tracking algorithm to solve the multi-speaker tracking problem.

Forecasting Pathogen Dynamics with Bayesian Model-Averaging: Application to Xylella fastidiosa.

Forecasting invasive-pathogen dynamics is paramount to anticipate eradication and containment strategies. Such predictions can be obtained using a model grounded on partial differential equations (PDE; often exploited to model invasions) and fitted to surveillance data. This framework allows the construction of phenomenological but concise models relying on mechanistic hypotheses and real observations. However, it may lead to models with overly rigid behavior and possible data-model mismatches. Hence, to avoid drawing a forecast grounded on a single PDE-based model that would be prone to errors, we propose to apply Bayesian model averaging (BMA), which allows us to account for both parameter and model uncertainties. Thus, we propose a set of different competing PDE-based models for representing the pathogen dynamics, we use an adaptive multiple importance sampling algorithm (AMIS) to estimate parameters of each competing model from surveillance data in a mechanistic-statistical framework, we evaluate the posterior probabilities of models by comparing different approaches proposed in the literature, and we apply BMA to draw posterior distributions of parameters and a posterior forecast of the pathogen dynamics. This approach is applied to predict the extent of Xylella fastidiosa in South Corsica, France, a phytopathogenic bacterium detected in situ in Europe less than 10 years ago (Italy 2013, France 2015). Separating data into training and validation sets, we show that the BMA forecast outperforms competing forecast approaches.

Daisee: Adaptive importance sampling by balancing exploration and exploitation

AbstractWe study adaptive importance sampling (AIS) as an online learning problem and argue for the importance of the trade‐off between exploration and exploitation in this adaptation. Borrowing ideas from the online learning literature, we propose Daisee, a partition‐based AIS algorithm. We further introduce a notion of regret for AIS and show that Daisee has cumulative pseudo‐regret, where is the number of iterations. We then extend Daisee to adaptively learn a hierarchical partitioning of the sample space for more efficient sampling and confirm the performance of both algorithms empirically.

MCMC‐driven importance samplers

Monte Carlo sampling methods are the standard procedure for approximating complicated integrals of multidimensional posterior distributions in Bayesian inference. In this work, we focus on the class of layered adaptive importance sampling algorithms, which is a family of adaptive importance samplers where Markov chain Monte Carlo algorithms are employed to drive an underlying multiple importance sampling scheme. The modular nature of the layered adaptive importance sampling scheme allows for different possible implementations, yielding a variety of different performances and computational costs. In this work, we propose different enhancements of the classical layered adaptive importance sampling setting in order to increase the efficiency and reduce the computational cost, of both upper and lower layers. The different variants address computational challenges arising in real-world applications, for instance with highly concentrated posterior distributions. Furthermore, we introduce different strategies for designing cheaper schemes, for instance, recycling samples generated in the upper layer and using them in the final estimators in the lower layer. Different numerical experiments show the benefits of the proposed schemes, comparing with benchmark methods presented in the literature, and in several challenging scenarios.

Importance Sampling with the Integrated Nested Laplace Approximation

The integrated nested Laplace approximation (INLA) is a deterministic approach to Bayesian inference on latent Gaussian models (LGMs) and focuses on fast and accurate approximation of posterior marginals for the parameters in the models. Recently, methods have been developed to extend this class of models to those that can be expressed as conditional LGMs by fixing some of the parameters in the models to descriptive values. These methods differ in the manner descriptive values are chosen. This article proposes to combine importance sampling with INLA (IS-INLA), and extends this approach with the more robust adaptive multiple importance sampling algorithm combined with INLA (AMIS-INLA). This article gives a comparison between these approaches and existing methods on a series of applications with simulated and observed datasets and evaluates their performance based on accuracy, efficiency, and robustness. The approaches are validated by exact posteriors in a simple bivariate linear model; then, they are applied to a Bayesian lasso model, a Poisson mixture, a zero-inflated Poisson model and a spatial autoregressive combined model. The applications show that the AMIS-INLA approach, in general, outperforms the other methods compared, but the IS-INLA algorithm could be considered for faster inference when good proposals are available. Supplementary materials for this article are available online.

A novel adaptive importance sampling algorithm for Bayesian model updating

Bayesian model updating has computational capability of reducing uncertainties in engineering models and yielding valuable inferences for model predictions from observed data. Importance sampling (IS) and Markov chain Monte Carlo (MCMC) are the two main techniques among the existing simulation-based methods for Bayesian model updating. Motivated by the fact IS outperforms MCMC in terms of computational efficiency once the proposal importance sampling density (ISD) is appropriately chosen, this paper proposes an innovative adaptive importance sampling (AIS) algorithm using Gaussian mixture to overcome the limitations of conventional IS-based methods. Integrating of the concepts of population Monte Carlo (PMC) and cross entropy (CE) contributes to the major novelty of the proposed algorithm. Consequently, the proposed AIS algorithm can successfully construct the ISD that resembles the sophisticated target posterior density. Moreover, a metric quantifying sampling effectiveness called normalized effective sample size (N-ESS) is also adopted to measure the similarity between the ISD and the target density. One benchmark example of system identification and one case study of chloride-induced concrete corrosion are investigated to demonstrate the accuracy and robustness of the proposed algorithm.

Power Grid Reliability Estimation via Adaptive Importance Sampling

Electricity production currently generates approximately 25% of greenhouse gas emissions in the USA. Thus, increasing the amount of renewable energy is a key step to carbon neutrality. However, integrating a large amount of fluctuating renewable generation is a significant challenge for power grid operating and planning. Grid reliability, i.e., an ability to meet operational constraints under power fluctuations, is probably the most important of them. In this letter, we propose computationally efficient and accurate methods to estimate the probability of line overflow, i.e., reliability constraints violation, under a known distribution of renewable energy generation. To this end, we investigate an importance sampling approach, a flexible extension of Monte-Carlo methods, which adaptively changes the sampling distribution to generate more samples near the reliability boundary. The approach allows to estimate overload probability in real-time based only on a few dozens of random samples, compared to thousands required by the plain Monte-Carlo. Our study focuses on high voltage direct current power transmission grids with linear reliability constraints on power injections and line currents. We propose a novel theoretically justified physics-informed adaptive importance sampling algorithm and compare its performance to state-of-the-art methods on multiple IEEE power grid test cases.

Integrating geostatistical maps and infectious disease transmission models using adaptive multiple importance sampling

The Adaptive Multiple Importance Sampling algorithm (AMIS) is an iterative technique which recycles samples from all previous iterations in order to improve the efficiency of the proposal distribution. We have formulated a new statistical framework, based on AMIS, to take the output from a geostatistical model of infectious disease prevalence, incidence or relative risk, and project it forward in time under a mathematical model for transmission dynamics. We adapted the AMIS algorithm so that it can sample from multiple targets simultaneously by changing the focus of the adaptation at each iteration. By comparing our approach against the standard AMIS algorithm, we showed that these novel adaptations greatly improve the efficiency of the sampling. We tested the performance of our algorithm on four case studies: ascariasis in Ethiopia, onchocerciasis in Togo, human immunodeficiency virus (HIV) in Botswana, and malaria in the Democratic Republic of the Congo.

MIFAS: Multi‐source heterogeneous information fusion with adaptive importance sampling for link prediction

AbstractLink prediction plays an important role in constructing knowledge graph. Recently, graph representation learning models yield state‐of‐the‐art results. However, existing models concentrate merely on triples or graph structures and mostly ignore textual descriptions, resulting in incomplete or partial information. In this paper, we propose a novel graph representation learning model to address this challenge, namely multi‐source heterogeneous information fusion with adaptive importance sampling. Our model leverages multiple sources, such triple, graph structure and textual description, and generate rich‐attribute embeddings for entities, encapsulating relations simultaneously. We also propose an adaptive importance sampling algorithm to boost aggregation of useful features from local neighbours. Additionally, we also boost node aggregation of useful features from local neighbours by adaptive importance sampling algorithm in our model. Experimental results on two benchmark datasets show that our proposed model significantly outperforms state‐of‐the‐art methods.

Safe adaptive importance sampling: A mixture approach

This paper investigates adaptive importance sampling algorithms for which the policy, the sequence of distributions used to generate the particles, is a mixture distribution between a flexible kernel density estimate (based on the previous particles), and a “safe” heavy-tailed density. When the share of samples generated according to the safe density goes to zero but not too quickly, two results are established: (i) uniform convergence rates are derived for the policy toward the target density; (ii) a central limit theorem is obtained for the resulting integral estimates. The fact that the asymptotic variance is the same as the variance of an “oracle” procedure with variance-optimal policy, illustrates the benefits of the approach. In addition, a subsampling step (among the particles) can be conducted before constructing the kernel estimate in order to decrease the computational effort without altering the performance of the method. The practical behavior of the algorithms is illustrated in a simulation study.

Policy Gradient Importance Sampling for Bayesian Inference

In this paper, we propose a novel adaptive importance sampling (AIS) algorithm for probabilistic inference. The sampler learns a proposal distribution adaptation strategy by framing AIS as a reinforcement learning problem. Under this structure, the proposal distribution of the sampler is treated as an agent whose state is controlled using a parameterized policy. At each iteration of the algorithm, the agent earns a reward that is related to its contribution to the variance of the AIS estimator of the normalization constant of the target distribution. Policy gradient methods are employed to learn a locally optimal policy that maximizes the expected value of the sum of all rewards. Numerical simulations on two different examples demonstrate promising results for the future application of the proposed method to complex Bayesian models.

A bayesian inference procedure based on inverse dispersion modelling for source term estimation in built-up environments

Abstract In atmospheric physics, reconstructing a pollution source is a challenging and important question. It provides better input parameters to dispersion models, and gives useful information to first-responder teams in case of an accidental toxic release. Various methods already exist, but using them requires an important amount of computational resources, especially when the accuracy of the dispersion model increases which is necessary in complex built-up environments. In this paper, a Bayesian probabilistic approach to estimate the location and the temporal emission profile of a pointwise source is proposed. More precisely, an Adaptive Multiple Importance Sampling (AMIS) algorithm is considered and enhanced by an efficient use of a Lagrangian Particle Dispersion Model (LPDM) in backward mode. Twin experiments empirically demonstrate the efficiency of the proposed inference strategy in very complex cases.

Bayesian Multiple Quantile Regression for Linear Models Using a Score Likelihood

We propose the use of a score based working likelihood function for quantile regression which can perform inference for multiple conditional quantiles of an arbitrary number. We show that the proposed likelihood can be used in a Bayesian framework leading to valid frequentist inference, whereas the commonly used asymmetric Laplace working likelihood leads to invalid interval estimations and requires further correction. For computation, we propose a novel adaptive importance sampling algorithm to compute important posterior summaries such as the posterior mean and the covariance matrix. Our proposed approach makes it feasible to perform valid inference for parameters such as the slope differences at different quantile levels, which is either not possible or cumbersome using existing Bayesian approaches. Empirical results demonstrate that the proposed likelihood has good estimation and inferential properties and that the proposed computational algorithm is more efficient than its competitors.

An Efficient Adaptive Importance Sampling Method for SRAM and Analog Yield Analysis

Performance failure has become a major threat for various memory and analog circuits. It is challenging to estimate the extremely small failure probability when failed samples are distributed in multiple disjoint regions. In this article, we propose an adaptive importance sampling (AIS) algorithm. AIS has several iterations of sampling region adjustments, while existing methods predecide a static sampling distribution. We design two adaptive frameworks based on resampling and population Metropolis–Hastings (MH) to iteratively search for failure regions. The experimental results of the AIS method exhibit better efficiency and higher accuracy. For SRAM bit cell with single failure region, the AIS method uses 2– $27{\times }$ fewer samples and reaches better accuracy when compared to several recent methods. For a two-stage amplifier circuit with multiple failure regions, the AIS method is $90{\times }$ faster than Monte Carlo and 7–23 ${\times }$ over other methods. For charge pump circuit and $C^{2}MOS$ master–slave latch circuit, the AIS method can reach 6– $18{\times }$ and 4– $6{\times }$ speedup over other methods, respectively.

Dating and localizing an invasion from post-introduction data and a coupled reaction\u2013diffusion\u2013absorption model

Invasion of new territories by alien organisms is of primary concern for environmental and health agencies and has been a core topic in mathematical modeling, in particular in the intents of reconstructing the past dynamics of the alien organisms and predicting their future spatial extents. Partial differential equations offer a rich and flexible modeling framework that has been applied to a large number of invasions. In this article, we are specifically interested in dating and localizing the introduction that led to an invasion using mathematical modeling, post-introduction data and an adequate statistical inference procedure. We adopt a mechanistic-statistical approach grounded on a coupled reaction–diffusion–absorption model representing the dynamics of an organism in an heterogeneous domain with respect to growth. Initial conditions (including the date and site of the introduction) and model parameters related to diffusion, reproduction and mortality are jointly estimated in the Bayesian framework by using an adaptive importance sampling algorithm. This framework is applied to the invasion of Xylella fastidiosa, a phytopathogenic bacterium detected in South Corsica in 2015, France.

An Automatic Adaptive Importance Sampling Algorithm for Molecular Dynamics in Reaction Coordinates

In this article, we propose an adaptive importance sampling scheme for dynamical quantities of complex systems, which are metastable. The main idea of this article is to combine metadynamics, an al...

Convergence analysis of adaptive biasing potential methods for diffusion processes

This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently sample the invariant distribution of the diffusion process, thanks to the approximation of the associated free energy function (relative to a reaction coordinate). The bias which is introduced in the dynamics is computed adaptively; it depends on the past of the trajectory of the process through some time-averages. We give a detailed and general construction of such methods. We prove the consistency of the approach (almost sure convergence of well-chosen weighted empirical probability distribution). We justify the efficiency thanks to several qualitative and quantitative additional arguments. To prove these results , we revisit and extend tools from stochastic approximation applied to self-interacting diffusions, in an original context.

A surrogate accelerated multicanonical Monte Carlo method for uncertainty quantification

In this work we consider a class of uncertainty quantification problems where the system performance or reliability is characterized by a scalar parameter y. The performance parameter y is random due to the presence of various sources of uncertainty in the system, and our goal is to estimate the probability density function (PDF) of y. We propose to use the multicanonical Monte Carlo (MMC) method, a special type of adaptive importance sampling algorithms, to compute the PDF of interest. Moreover, we develop an adaptive algorithm to construct local Gaussian process surrogates to further accelerate the MMC iterations. With numerical examples we demonstrate that the proposed method can achieve several orders of magnitudes of speedup over the standard Monte Carlo methods.

Estimation of a launch vehicle stage fallout zone with parametric and non-parametric importance sampling algorithms in presence of uncertain input distributions

The estimation of launch vehicle fall back safety zone is a crucial problem in space application since the consequence of a mistake may be dramatic for the population. It consists in estimating the probability that the distance between the launcher stage fall-back position calculated, with a trajectory simulation code, and the predicted one is lower than a given threshold. This probability of having a distance that exceeds the critical limit is of course low and may hardly be estimated with crude Monte Carlo methods. One proposes in this paper adaptive importance sampling algorithms when some parameters of input probability density suffer from uncertainty. This situation is a difficult issue for computational reasons since a complete importance sampling procedure is necessary to estimate the rare event probability associated to each combination of input density parameters. It is no more the case with the proposed parametric and non-parametric approaches based on the definition of a more adapted initial sampling density.

An adaptive importance sampling algorithm for Bayesian inversion with multimodal distributions

Parametric uncertainties are encountered in the simulations of many physical systems, and may be reduced by an inverse modeling procedure that calibrates the simulation results to observations on the real system being simulated. Following Bayes' rule, a general approach for inverse modeling problems is to sample from the posterior distribution of the uncertain model parameters given the observations. However, the large number of repetitive forward simulations required in the sampling process could pose a prohibitive computational burden. This difficulty is particularly challenging when the posterior is multimodal. We present in this paper an adaptive importance sampling algorithm to tackle these challenges. Two essential ingredients of the algorithm are: 1) a Gaussian mixture (GM) model adaptively constructed as the proposal distribution to approximate the possibly multimodal target posterior, and 2) a mixture of polynomial chaos (PC) expansions, built according to the GM proposal, as a surrogate model to alleviate the computational burden caused by computational-demanding forward model evaluations. In three illustrative examples, the proposed adaptive importance sampling algorithm demonstrates its capabilities of automatically finding a GM proposal with an appropriate number of modes for the specific problem under study, and obtaining a sample accurately and efficiently representing the posterior with limited number of forward simulations.