Importance Sampling Step Research Articles

A physics and data co-driven surrogate modeling method for high-dimensional rare event simulation

This paper presents a physics and data co-driven surrogate modeling method for efficient rare event simulation of civil and mechanical systems with high-dimensional input uncertainties. The method fuses interpretable low-fidelity physical models with data-driven error corrections. The hypothesis is that a well-designed and well-trained simplified physical model can preserve salient features of the original model, while data-fitting techniques can fill the remaining gaps between the surrogate and original model predictions. The coupled physics-data-driven surrogate model is adaptively trained using active learning, aiming to achieve a high correlation and small bias between the surrogate and original model responses in the critical parametric region of a rare event. A final importance sampling step is introduced to correct the surrogate model-based probability estimations. Static and dynamic problems with input uncertainties modeled by random field and stochastic process are studied to demonstrate the proposed method.

Backward Importance Sampling for Online Estimation of State Space Models

This article proposes a new Sequential Monte Carlo algorithm to perform online estimation in the context of state space models when either the transition density of the latent state or the conditional likelihood of an observation given a state is intractable. In this setting, obtaining low variance estimators of expectations under the posterior distributions of the unobserved states given the observations is a challenging task. Following recent theoretical results for pseudo-marginal sequential Monte Carlo smoothers, a pseudo-marginal backward importance sampling step is introduced to estimate such expectations. This new step allows to reduce very significantly the computational time of the existing numerical solutions based on an acceptance–rejection procedure for similar performance, and to broaden the class of eligible models for such methods. For instance, in the context of multivariate stochastic differential equations, the proposed algorithm makes use of unbiased estimates of the unknown transition densities under much weaker assumptions than most standard alternatives. The performance of this estimator is assessed for high-dimensional discrete-time latent data models, for recursive maximum likelihood estimation in the context of Partially Observed Diffusion process (POD), and in the case of a bidimensional partially observed stochastic Lotka-Volterra model. Supplementary materials for this article are available online.

CELL TRACKING USING PARTICLE FILTERS WITH IMPLICIT CONVEX SHAPE MODEL IN 4D CONFOCAL MICROSCOPY IMAGES.

Bayesian frameworks are commonly used in tracking algorithms. An important example is the particle filter, where a stochastic motion model describes the evolution of the state, and the observation model relates the noisy measurements to the state. Particle filters have been used to track the lineage of cells. Propagating the shape model of the cell through the particle filter is beneficial for tracking. We approximate arbitrary shapes of cells with a novel implicit convex function. The importance sampling step of the particle filter is defined using the cost associated with fitting our implicit convex shape model to the observations. Our technique is capable of tracking the lineage of cells for nonmitotic stages. We validate our algorithm by tracking the lineage of retinal and lens cells in zebrafish embryos.

On the stability of sequential Monte Carlo methods in high dimensions

We investigate the stability of a Sequential Monte Carlo (SMC) method applied to the problem of sampling from a target distribution on Rd for large d. It is well known [Bengtsson, Bickel and Li, In Probability and Statistics: Essays in Honor of David A. Freedman, D. Nolan and T. Speed, eds. (2008) 316–334 IMS; see also Pushing the Limits of Contemporary Statistics (2008) 318–32 9 IMS, Mon. Weather Rev. (2009) 136 (2009) 4629–4640] that using a single importance sampling step, one produces an approximation for the target that deteriorates as the dimension d increases, unless the number of Monte Carlo samples N increases at an exponential rate in d. We show that this degeneracy can be avoided by introducing a sequence of artificial targets, starting from a “simple” density and moving to the one of interest, using an SMC method to sample from the sequence; see, for example, Chopin [Biometrika 89 (2002) 539–551]; see also [J. R. Stat. Soc. Ser. B Stat. Methodol. 68 (2006) 411–436, Phys. Rev. Lett. 78 (1997) 2690–2693, Stat. Comput. 11 (2001) 125–139]. Using this class of SMC methods with a fixed number of samples, one can produce an approximation for which the effective sample size (ESS) converges to a random variable eN as d → ∞ with 1 < eN < N. The convergence is achieved with a computational cost proportional to Nd2. If eN � N, we can raise its value by introducing a number of resampling steps, say m (where m is independent of d). In this case, the ESS converges to a random variable eN,m as d → ∞ and limm→∞ eN,m = N. Also, we show that the Monte Carlo error for estimating a fixed-dimensional marginal expectation is of order √ 1 N uniformly in d. The results imply that, in high dimensions, SMC algorithms can efficiently control the variability of the importance sampling weights and estimate fixed-dimensional marginals at a cost which is less than exponential in d and indicate that resampling leads to a reduction in the Monte Carlo error and increase in the ESS. All of our analysis is made under the assumption that the target density is i.i.d.

Face Tracking Based on Particle Filter with Multi-feature Fusion

Traditional particle filter cannot accommodate to the environment of background interferences, illumination variations and occlusions. This paper presents a face tracking method with fusion of color histogram, contour features and grey model based on particle filter. First, it brought in contour features as the main cue of multiple features when tracking the face without stable color histogram. Then, as prior information was neglected in traditional particle filter, this paper employed GM(1,1) model to yield proposal distribution, such that the proposal distribution would bear a higher approximation to posterior probability. Finally, in the importance sampling step, sampling was corresponded to the particle weight in case of the particle degradation. The experiments show that our method outperformed the previous with more accuracy and flexibility, particularly under the condition of color background interferences, drastic illumination variations and complete occlusions. DOI : http://dx.doi.org/10.11591/telkomnika.v12i1.3381

Free energy methods for Bayesian inference: efficient exploration of univariate Gaussian mixture posteriors

Because of their multimodality, mixture posterior distributions are difficult to sample with standard Markov chain Monte Carlo (MCMC) methods. We propose a strategy to enhance the sampling of MCMC in this context, using a biasing procedure which originates from computational Statistical Physics. The principle is first to choose a coordinate, that is, a direction in which the target distribution is multimodal. In a second step, the marginal log-density of the reaction coordinate with respect to the posterior distribution is estimated; minus this quantity is called free energy in the computational Statistical Physics literature. To this end, we use adaptive biasing Markov chain algorithms which adapt their targeted invariant distribution on the fly, in order to overcome sampling barriers along the chosen reaction coordinate. Finally, we perform an importance sampling step in order to remove the bias and recover the true posterior. The efficiency factor of the importance sampling step can easily be estimated a priori once the bias is known, and appears to be rather large for the test cases we considered. A crucial point is the choice of the reaction coordinate. One standard choice (used for example in the classical Wang-Landau algorithm) is minus the log-posterior density. We discuss other choices. We show in particular that the hyper-parameter that determines the order of magnitude of the variance of each component is both a convenient and an efficient reaction coordinate. We also show how to adapt the method to compute the evidence (marginal likelihood) of a mixture model. We illustrate our approach by analyzing two real data sets.

Behavior Extraction from Examples Using Federate MCMC-Based Particle Filtering

Data-driven methods of simulating a crowd of virtual humans that exhibit behaviors imitating real human crowds play an important role in crowd simulation. In this paper, we propose a Bayesian framework for the extraction of real human's behaviors which exhibit interactions in their daily life using multiple fixed cameras. The described Markov chain Monte Carlo particle filter can effectively deals with interacting targets which are influenced by the proximity and behaviors of other targets. In this paper, we use a Markov random field motion prior combing with a federate filter algorithm which treats the observations discriminatorily to substantially improve the tracking of a fixed number of interacting targets. Simultaneously, we replace the traditional importance sampling step with MCMC sampling step to get over the vast computational requirements for large numbers of targets. i.e., we focus on the data fusion and the behavior recognition process. Finally, experimental results demonstrate that the proposed Bayesian framework deals efficiently and effectively with extractions of interacting behavior.

A Non-stationary Noise Suppression Method Based on Particle Filtering and Polyak Averaging

This paper addresses a speech recognition problem in non-stationary noise environments: the estimation of noise sequences. To solve this problem, we present a particle filter-based sequential noise estimation method for front-end processing of speech recognition in noise. In the proposed method, a noise sequence is estimated in three stages: a sequential importance sampling step, a residual resampling step, and finally a Markov chain Monte Carlo step with Metropolis-Hastings sampling. The estimated noise sequence is used in the MMSE-based clean speech estimation. We also introduce Polyak averaging and feedback into a state transition process for particle filtering. In the evaluation results, we observed that the proposed method improves speech recognition accuracy in the results of non-stationary noise environments a noise compensation method with stationary noise assumptions.

MCMC-based particle filtering for tracking a variable number of interacting targets

We describe a particle filter that effectively deals with interacting targets--targets that are influenced by the proximity and/or behavior of other targets. The particle filter includes a Markov random field (MRF) motion prior that helps maintain the identity of targets throughout an interaction, significantly reducing tracker failures. We show that this MRF prior can be easily implemented by including an additional interaction factor in the importance weights of the particle filter. However, the computational requirements of the resulting multitarget filter render it unusable for large numbers of targets. Consequently, we replace the traditional importance sampling step in the particle filter with a novel Markov chain Monte Carlo (MCMC) sampling step to obtain a more efficient MCMC-based multitarget filter. We also show how to extend this MCMC-based filter to address a variable number of interacting targets. Finally, we present both qualitative and quantitative experimental results, demonstrating that the resulting particle filters deal efficiently and effectively with complicated target interactions.