Sequential Monte Carlo Methodology Research Articles

Parallel sequential Monte Carlo for stochastic gradient-free nonconvex optimization

We introduce and analyze a parallel sequential Monte Carlo methodology for the numerical solution of optimization problems that involve the minimization of a cost function that consists of the sum of many individual components. The proposed scheme is a stochastic zeroth-order optimization algorithm which demands only the capability to evaluate small subsets of components of the cost function. It can be depicted as a bank of samplers that generate particle approximations of several sequences of probability measures. These measures are constructed in such a way that they have associated probability density functions whose global maxima coincide with the global minima of the original cost function. The algorithm selects the best performing sampler and uses it to approximate a global minimum of the cost function. We prove analytically that the resulting estimator converges to a global minimum of the cost function almost surely and provide explicit convergence rates in terms of the number of generated Monte Carlo samples and the dimension of the search space. We show, by way of numerical examples, that the algorithm can tackle cost functions with multiple minima or with broad “flat” regions which are hard to minimize using gradient-based techniques.

THE POTENTIAL APPROACH IN PRACTICE

This paper studies the fitting of Markov chain potential models to interest-rate derivative prices in four currencies simultaneously, using sequential Monte Carlo methodology (particle filtering). The potential approach starts from some Markov process which is supposed to drive the random observations, and there have been many studies where this Markov process is taken to be a diffusion; fewer studies have worked from a finite-state Markov chain, and this seems to be the first study to attempt to fit such models to data. With the available data, we show impressive agreement of the fitted models with market prices.

Coupling stochastic EM and approximate Bayesian computation for parameter inference in state-space models

We study the class of state-space models and perform maximum likelihood estimation for the model parameters. We consider a stochastic approximation expectation–maximization (SAEM) algorithm to maximize the likelihood function with the novelty of using approximate Bayesian computation (ABC) within SAEM. The task is to provide each iteration of SAEM with a filtered state of the system, and this is achieved using an ABC sampler for the hidden state, based on sequential Monte Carlo methodology. It is shown that the resulting SAEM-ABC algorithm can be calibrated to return accurate inference, and in some situations it can outperform a version of SAEM incorporating the bootstrap filter. Two simulation studies are presented, first a nonlinear Gaussian state-space model then a state-space model having dynamics expressed by a stochastic differential equation. Comparisons with iterated filtering for maximum likelihood inference, and Gibbs sampling and particle marginal methods for Bayesian inference are presented.

Sequential Monte Carlo for fractional stochastic volatility models

In this paper, we consider a fractional stochastic volatility model, that is a model in which the volatility may exhibit a long-range dependent or a rough/antipersistent behaviour. We propose a dynamic sequential Monte Carlo methodology that is applicable to both long memory and antipersistent processes in order to estimate the volatility as well as the unknown parameters of the model. We establish a central limit theorem for the state and parameter filters and we study asymptotic properties (consistency and asymptotic normality) for the filter. We illustrate our results with a simulation study and we apply our method to estimate the volatility and the parameters of a long-range dependent model for S& P 500 data.

A multi-model sequential Monte Carlo methodology for indoor tracking: Algorithms and experimental results

In this paper we address the problem of indoor tracking using received signal strength (RSS) as a position-dependent data measurement. Since RSS is highly influenced by multipath propagation, it turns out very hard to adequately model the correspondence between the received power and the transmitter-to-receiver distance. Although various models have been proposed in the literature, they often require the use of very large collections of data in order to fit them and display great sensitivity to changes in the radio propagation environment. In this work we advocate the use of switching multiple models that account for different classes of target dynamics and propagation environments and propose a flexible probabilistic switching scheme. The resulting state-space structure is termed a generalized switching multiple model (GSMM) system. Within this framework, we investigate two types of models for the RSS data: polynomial models and classical logarithmic path-loss representation. The first model is more accurate however it demands an offline model fitting step. The second one is less precise but it can be fitted in an online procedure. We have designed two tracking algorithms built around a Rao-Blackwellized particle filter, tailored to the GSMM structure and assessed its performances both with synthetic and experimental measurements.

Les douleurs d’avulsion du plexus brachial

We investigate a recently proposed sequential Monte Carlo methodology for recursively tracking the minima of a cost function that evolves with time. These methods, subsequently referred to as sequential Monte Carlo minimization (SMCM) procedures, have an algorithmic structure similar to particle filters: they involve the generation of random paths in the space of the signal of interest (SoI), the stochastic selection of the fittest paths and the ranking of the survivors according to their cost. In this paper, we propose an extension of the original SMCM methodology (that makes it applicable to a broader class of cost functions) and introduce an asymptotic-convergence analysis. Our analytical results are based on simple induction arguments and show how the SoI-estimates computed by a SMCM algorithm converge, in probability, to a sequence of minimizers of the cost function. We illustrate these results by means of two computer simulation examples.

Analysis of a sequential Monte Carlo method for optimization in dynamical systems

We investigate a recently proposed sequential Monte Carlo methodology for recursively tracking the minima of a cost function that evolves with time. These methods, subsequently referred to as sequential Monte Carlo minimization (SMCM) procedures, have an algorithmic structure similar to particle filters: they involve the generation of random paths in the space of the signal of interest (SoI), the stochastic selection of the fittest paths and the ranking of the survivors according to their cost. In this paper, we propose an extension of the original SMCM methodology (that makes it applicable to a broader class of cost functions) and introduce an asymptotic-convergence analysis. Our analytical results are based on simple induction arguments and show how the SoI-estimates computed by a SMCM algorithm converge, in probability, to a sequence of minimizers of the cost function. We illustrate these results by means of two computer simulation examples.

Sequential Monte Carlo Methods for Joint Detection and Tracking of Multiaspect Targets in Infrared Radar Images

We present in this paper a sequential Monte Carlo methodology for joint detection and tracking of a multiaspect target in image sequences. Unlike the traditional contact/association approach found in the literature, the proposed methodology enables integrated, multiframe target detection and tracking incorporating the statistical models for target aspect, target motion, and background clutter. Two implementations of the proposed algorithm are discussed using, respectively, a resample-move (RS) particle filter and an auxiliary particle filter (APF). Our simulation results suggest that the APF configuration outperforms slightly the RS filter in scenarios of stealthy targets.

A non-resampling sequential monte carlo detector for coded OFDM systems based on periodic termination of differential phase trellis

Sequential Monte Carlo (SMC) is a group of methods that use Monte Carlo simulation to solve online estimation problems in dynamic systems. SMC methods are traditionally built on the techniques of sequential importance sampling (SIS) and resampling. In this paper, we apply the SMC methodology to the problem of symbol detection in a differentially encoded orthogonal frequency division multiplexing (OFDM) system over a frequency selective fading channel. We first propose the periodical termination of differential phase trellis at predetermined indices. It is seen that accelerated weight degeneracy and impoverished trajectory diversity - problems that are encountered in traditional SMC methods - are mitigated. Using these observations, a novel SMC framework that circumvents resampling is then developed. The effect of varying termination periods on the performance of the non-resampling detector is investigated. We also present results which show that periodic termination helps to retard weight degeneracy. The performance of traditional and non-resampling SMC detectors for a convolutional-coded OFDM system is compared and simulation results suggest that the non-resampling detector performs better than its traditional counterpart. We also consider a low-density parity check (LDPC)-coded OFDM system and simulation results suggest the near bound performance of the proposed non-resampling SMC detector

Wavelet-Based Sequential Monte Carlo Blind Receivers in Fading Channels With Unknown Channel Statistics

Recently, an adaptive Bayesian receiver for blind detection in flat-fading channels was developed by the present authors, based on the sequential Monte Carlo methodology. That work is built on a parametric modeling of the fading process in the form of a state-space model and assumes the knowledge of the second-order statistics of the fading channel. In this paper, we develop a nonparametric approach to the problem of blind detection in fading channels, without assuming any knowledge of the channel statistics. The basic idea is to decompose the fading process using a wavelet basis and to use the sequential Monte Carlo technique to track both the wavelet coefficients and the transmitted symbols. A novel resampling-based wavelet shrinkage technique is proposed to dynamically choose the number of wavelet coefficients to best fit the fading process. Under such a framework, blind detectors for both flat-fading channels and frequency-selective fading channels are developed. Simulation results are provided to demonstrate the excellent performance of the proposed blind adaptive receivers.

Nonparametric adaptive detection in fading channels based on sequential Monte Carlo and Bayesian model averaging

Recently, a Bayesian receiver for blind detection in fading channels has been proposed by Chen, Wang and Liu (200,IEEE Trans. Inform. Theory,46, 2079–2094), based on the sequential Monte Carlo methodology. That work is built on a parametric modelling of the fading process in the form of a state-space model, and assumes the knowledge of the second-order statistics of the fading channel. In this paper, we develop a nonparametric approach to the problem of blind detection in fading channels, without assuming any knowledge of the channel statistics. The basic idea is to decompose the fading process using a wavelet basis, and to use the sequential Monte Carlo technique to track both the wavelet coefficients and the transmitted symbols. Moreover, the algorithm is adaptive to time varying speed/smoothness in the fading process and the uncertainty on the number of wavelet coefficients (shrinkage order) needed. Simulation results are provided to demonstrate the excellent performance of the proposed blind adaptive receivers.

Adaptive joint detection and decoding in flat-fading channels via mixture Kalman filtering

A novel adaptive Bayesian receiver for signal detection and decoding in fading channels with known channel statistics is developed; it is based on the sequential Monte Carlo methodology that has emerged in the field of statistics. The basic idea is to treat the transmitted signals as "missing data" and to sequentially impute multiple samples of them based on the observed signals. The imputed signal sequences, together with their importance weights, provide a way to approximate the Bayesian estimate of the transmitted signals and the channel states. Adaptive receiver algorithms for both uncoded and convolutionally coded systems are developed. The proposed techniques can easily handle the non-Gaussian ambient channel noise. It is shown through simulations that the proposed sequential Monte Carlo receivers achieve near-bound performance in fading channels for both uncoded and coded systems, without the use of any training/pilot symbols or decision feedback. Moreover, the proposed receiver structure exhibits massive parallelism and is ideally suited for high-speed parallel implementation using the very large scale integration (VLSI) systolic array technology.