Particle Filtering

This paper addresses the problem of tracking multiple pedestrians whose motion is dependent on one another. The behavior of a pedestrian may be often affected by the motion of other pedestrians, obstacles in the surrounding, and his/her intended destination. Hence, a motion modeling technique, which integrates the various factors that affect the motion of pedestrians, is needed. In this paper, a social force based motion model integrated into the probability hypothesis density (PHD) framework is proposed. The social force concept has previously been used to model pedestrian motion when there are interactions among pedestrians. In this paper, the sequential Monte Carlo (SMC) technique and the Gaussian mixture (GM) technique are used to implement the proposed Social Force PHD (SF-PHD) filter and its multiple model variant in pedestrian tracking scenarios. A particle labeling approach is used in the SMC technique while a Gaussian component labeling approach is used in the GM technique for this purpose. Also, a modified performance measure independent of the proposed approaches but based on the posterior Cramer–Rao lower bound for targets whose motion is dependent on one another is derived. Simulation and real data-based results show that both the SMC implementation and the GM implementation of the proposed SF-PHD filter outperform existing filters that assume independent motion among ground targets.

Decision-making processes in medicine rely increasingly on modelling and simulation techniques; they are especially useful when combining evidence from multiple sources. Markov models are frequently used to synthesize the available evidence for such simulation studies, by describing disease and treatment progress, as well as associated factors such as the treatment's effects on a patient's life and the costs to society. When the same decision problem is investigated by multiple stakeholders, differing modelling assumptions are often applied, making synthesis and interpretation of the results difficult. This paper proposes a standardized approach towards the creation of Markov models. It introduces the notion of ‘general Markov models’, providing a common definition of the Markov models that underlie many similar decision problems, and develops a language for their specification. We demonstrate the application of this language by developing a general Markov model for adverse event analysis in radiotherapy and argue that the proposed method can automate the creation of Markov models from existing data. The approach has the potential to support the radiotherapy community in conducting systematic analyses involving predictive modelling of existing and upcoming radiotherapy data. We expect it to facilitate the application of modelling techniques in medical decision problems beyond the field of radiotherapy, and to improve the comparability of their results.

Nonlinear state-space models are ubiquitous in modeling real-world dynamical systems. Sequential Monte Carlo (SMC) techniques, also known as particle methods, are a well-known class of parameter estimation methods for this general class of state-space models. Existing SMC-based techniques rely on excessive sampling of the parameter space, which makes their computation intractable for large systems or tall data sets. Bayesian optimization techniques have been used for fast inference in state-space models with intractable likelihoods. These techniques aim to find the maximum of the likelihood function by sequential sampling of the parameter space through a single SMC approximator. Various SMC approximators with different fidelities and computational costs are often available for sample-based likelihood approximation. In this paper, we propose a multi-fidelity Bayesian optimization algorithm for the inference of general nonlinear state-space models (MFBO-SSM), which enables simultaneous sequential selection of parameters and approximators. The accuracy and speed of the algorithm are demonstrated by numerical experiments using synthetic gene expression data from a gene regulatory network model and real data from the VIX stock price index.

This paper describes a Bayesian approach to determining the order of a finite state Markov chain whose transition probabilities are themselves governed by a homogeneous finite state Markov chain. It extends previous work on homogeneous Markov chains to more general and applicable hidden Markov models. The method we describe uses a Markov chain Monte Carlo algorithm to obtain samples from the (posterior) distribution for both the order of Markov dependence in the observed sequence and the other governing model parameters. These samples allow coherent inferences to be made straightforwardly in contrast to those which use information criteria. The methods are illustrated by their application to both simulated and real data sets.

Position estimation in localization and tracking is often approached with Bayesian filtering. In combination with Gaussian assumptions about state distributions this approach results in efficient algorithms such as the Kalman filter. Indoors, however, the location state space is naturally constrained by walls and other obstacles that cannot be taken into account with Kalman or other Gaussian filters. More general Hidden Markov Models (HMMs) on the other hand do not make restrictive assumptions and thus allow for extensive explicit modelling. In particular for indoor positioning, we show how to inject geometric apriori knowledge, i.e. a given floor plan, into the parameters of a discrete-state HMM. In contrast to classical position estimation, we use an adapted Viterbi-algorithm for decoding the maximum aposteriori (MAP) trajectory estimate based on the geometry-aware HMM. Results and advantages of the presented method are discussed for the localization of a mobile sensor node in a simulated measurement setup.

The goal of this communication is to present a weighted likelihood discriminant for minimum error shape classification. Different from traditional maximum likelihood (ML) methods in which classification is carried out based on probabilities from independent individual class models as is the case for general hidden Markov model (HMM) methods, our proposed method utilizes information from all classes to minimize classification error. Proposed approach uses a hidden Markov model as a curvature feature based 2D shape descriptor. In this contribution we present a generalized probabilistic descent (GPD) method to weight the curvature likelihoods to achieve a discriminant function with minimum classification error. In contrast with other approaches, a weighted likelihood discriminant function is introduced. We believe that our sound theory based implementation reduces classification error by combining hidden Markov model with generalized probabilistic descent theory. We show comparative results obtained with our approach and classic maximum-likelihood calculation for fighter planes in terms of classification accuracies

Leroux's method for general hidden Markov models

In this paper, we address the problem of reduced-complexity estimation of general large-scale hidden Markov models with underlying nearly completely decomposable discrete-time Markov chains and finite-state outputs. An algorithm is presented that computes O(e) (where e is the related weak coupling parameter) approximations to the aggregate and full-order filtered estimates with substantial computational savings. These savings are shown to be quite large when the chains have blocks with small individual dimensions. Some simulation studies are presented to demonstrate the performance of the algorithm.

In this paper, we present a new method to analyze the throughput and delay of the selective-repeat (SR) automatic repeat-request (ARQ) protocol. Previous work on SR ARQ has concentrated on reliable feedback or two-state Markovian feedback errors. We solve a wider class of problems by characterizing both the forward and reverse channels by general hidden Markov models (HMMs). The moment-generating function (MGF) technique is used to find throughput and delay. To calculate the MGF, we construct matrix signal-flow graphs for the hidden Markov process. This procedure can be useful for a variety of other HMM problems, and is of interest by itself. Practical issues such as erasure errors and timeouts are included in our analyses, which are verified by extensive simulations

This paper is motivated by networked control systems deployed in a large-scale sensor network where data collection from all sensors is prohibitive. We model it as a class of discrete-time stochastic control systems for which the observations available to the controller are not fixed, but there are a number of options to choose from, and each choice has a cost associated with it. The observation costs are added to the running cost of the optimization criterion and the resulting optimal control problem is investigated. Since only part of the observations are available at each time step, the controller has to balance the system performance with the penalty of the requested information (query). We first formulate the problem for a general partially observed Markov decision process model and then specialize to the stochastic linear quadratic Gaussian problem. We focus primarily on the ergodic control problem and analyze this in detail.

Collected data have been evaluated and analyzed with the methods indicated below, using different mathematical/statistical tools, e. g. Matlab, Weka (machine learning software), HTK (Hidden Markov Model toolkit), RapidMiner (formerly known as YALE – Yet Another Learning Environment), the Unscrambler (software package for multivariate analysis and experimental design), LIBSVM (Library for Support Vector Machines), and GHMM (General Hidden Markov Model library).KeywordsHide Markov ModelLinear Discriminant AnalysisDifference ThresholdWeber FractionJust Noticeable DifferenceThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

A Unified Framework for Computing Regime-Switching Models

Prediction of Subcellular Localization of Eukaryotic Proteins Using Position-Specific Profiles and Neural Network with Weighted Inputs

Asymptotic theory plays a fundamental role in the developments of modern statistics, especially in the theoretical analysis of new methodologies. Some asymptotic results may borrow directly from the limit theory in probability, but many need deep insights of statistical contents and more accurate approximations, which have in turn fostered further developments of limit theory in probability. Peter Bickel has made far-reaching and wide-ranging contributions to modern statistics. He is a giant in theoretical statistics. In asymptotic theory, besides his contributions to bootstrap and high-dimensional statistical inference, in this paper I shall focus on four of his seminal papers on asymptotic expansions and Bartlett correction for Bayes solutions, likelihood ratio statistics and maximum-likelihood estimator for general hidden Markov models. The papers will be reviewed in chronological order.KeywordsHide Markov ModelAsymptotic DistributionAsymptotic TheoryAsymptotic NormalityLikelihood Ratio StatisticThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

We present a C++ library for constructing and analyzing general hidden Markov models. The library consists of a number of template classes and generic functions, parameterized with the precision of floating point types and different types of hardware acceleration.