SMC methods to avoid self-resolving for online Bayesian parameter estimation

Abstract—The particle filter is a powerful filtering technique that is able to handle a broad scope of nonlinear problems. However, it has also limitations: a standard particle filter is unable to handle, for instance, systems that include static variables (parameters) to be estimated together with the dynamic states. This limitation is due to the well-known “self-resolving” phenomenon, which is caused by the gradual loss of information that occurs during the resampling steps. In the context of online Bayesian parameter estimation, some approaches to handle this problem have proposed, such as adding artificial dynamics to the parameter model. However, these approaches typically both introduce new parameters (e.g. the intensity of artificial process noise) and inherent biases to the estimation problem. In this paper, we will give a give a look at two Sequential Monte Carlo techniques that do not rely on biasing the system model: the Autonomous Multiple Model particle filter and the Rao-Blackwellized Marginal particle filter. These approaches are not new, but have not been applied yet to the problem of online Bayesian parameter estimation for non-structured models. We will derive suitable adaptations of these methods for this problem and evaluate them using simulations. I

Labeling Uncertainty in Multitarget Tracking

In multitarget tracking, the problem of track labeling (assigning labels to tracks) is an ongoing research topic. The existing literature, however, lacks an appropriate measure of uncertainty related to the assigned labels that has a sound mathematical basis as well as clear practical meaning to the user. This is especially important in a situation where well separated targets move in close proximity with each other and thereafter separate again; in such a situation, it is well known that there will be confusion on target identities, also known as "mixed labeling." In this paper, we specify comprehensively the necessary assumptions for a Bayesian formulation of the multitarget tracking and labeling (MTTL) problem to be meaningful. We provide a mathematical characterization of the labeling uncertainties with clear physical interpretation. We also propose a novel labeling procedure that can be used in combination with any existing (unlabeled) MTT algorithm to obtain a Bayesian solution to the MTTL problem. One advantage of the resulting solution is that it readily provides the labeling uncertainty measures. Using the mixed labeling phenomenon in the presence of two targets as our test bed, we show with simulation results that an unlabeled multitarget sequential Monte Carlo (M-SMC) algorithm that employs sequential importance resampling (SIR) augmented with our labeling procedure performs much better than its "naive" extension, the labeled SIR M-SMC filter

Deep reinforcement learning for quantum multiparameter estimation

Estimation of physical quantities is at the core of most scientific research, and the use of quantum devices promises to enhance its performances. In real scenarios, it is fundamental to consider that resources are limited, and Bayesian adaptive estimation represents a powerful approach to efficiently allocate, during the estimation process, all the available resources. However, this framework relies on the precise knowledge of the system model, retrieved with a fine calibration, with results that are often computationally and experimentally demanding. We introduce a model-free and deep-learning-based approach to efficiently implement realistic Bayesian quantum metrology tasks accomplishing all the relevant challenges, without relying on any a priori knowledge of the system. To overcome this need, a neural network is trained directly on experimental data to learn the multiparameter Bayesian update. Then the system is set at its optimal working point through feedback provided by a reinforcement learning algorithm trained to reconstruct and enhance experiment heuristics of the investigated quantum sensor. Notably, we prove experimentally the achievement of higher estimation performances than standard methods, demonstrating the strength of the combination of these two black-box algorithms on an integrated photonic circuit. Our work represents an important step toward fully artificial intelligence-based quantum metrology

A Bayesian solution to multi-target tracking problems with mixed labelling

In Multi-Target Tracking (MTT), the problem of assigning labels to tracks (track labelling) is vastly covered in literature and has been previously formulated using Bayesian recursion. However, the existing literature lacks an appropriate measure of uncertainty related to the assigned labels which has sound mathematical basis and clear practical meaning (to the user). This is especially important in a situation where targets move in close proximity with each other and thereafter separate again. Because, in such a situation it is well-known that there will be confusion on target identities, also known as “mixed labelling‿. In this paper, we provide a mathematical characterization of the labelling uncertainties present in Bayesian multi-target tracking and labelling (MTTL) problems and define measures of labelling uncertainties with clear physical interpretation. The introduced uncertainty measures can be used to find the optimal track label assignment, and evaluate track labelling performance. We also analyze in details the mixed labelling phenomenon in the presence of two targets. In addition, we propose a new Sequential Monte Carlo (SMC) algorithm, the Labelling Uncertainty Aware Particle Filter (LUA-PF), for the multi target tracking and labelling problem that can provide good estimates of the uncertainty measures. We validate this using simulation and show that the proposed method performs much better when compared with the performance of the SIR multi-target SMC filter

Bayesian Inference for Genomic Data Analysis

High-throughput genomic data contain gazillion of information that are influenced by the complex biological processes in the cell. As such, appropriate mathematical modeling frameworks are required to understand the data and the data generating processes. This dissertation focuses on the formulation of mathematical models and the description of appropriate computational algorithms to obtain insights from genomic data. Specifically, characterization of intra-tumor heterogeneity is studied. Based on the total number of allele copies at the genomic locations in the tumor subclones, the problem is viewed from two perspectives: the presence or absence of copy-neutrality assumption. With the presence of copy-neutrality, it is assumed that the genome contains mutational variability and the three possible genotypes may be present at each genomic location. As such, the genotypes of all the genomic locations in the tumor subclones are modeled by a ternary matrix. In the second case, in addition to mutational variability, it is assumed that the genomic locations may be affected by structural variabilities such as copy number variation (CNV). Thus, the genotypes are modeled with a pair of (Q + 1)-ary matrices. Using the categorical Indian buffet process (cIBP), state-space modeling framework is employed in describing the two processes and the sequential Monte Carlo (SMC) methods for dynamic models are applied to perform inference on important model parameters. Moreover, the problem of estimating gene regulatory network (GRN) from measurement with missing values is presented. Specifically, gene expression time series data may contain missing values for entire expression values of a single point or some set of consecutive time points. However, complete data is often needed to make inference on the underlying GRN. Using the missing measurement, a dynamic stochastic model is used to describe the evolution of gene expression and point-based Gaussian approximation (PBGA) filters with one-step or two-step missing measurements are applied for the inference. Finally, the problem of deconvolving gene expression data from complex heterogeneous biological samples is examined, where the observed data are a mixture of different cell types. A statistical description of the problem is used and the SMC method for static models is applied to estimate the cell-type specific expressions and the cell type proportions in the heterogeneous samples

Characterization of uncertainty in Bayesian estimation using sequential Monte Carlo methods

In estimation problems, accuracy of the estimates of the quantities of interest cannot be taken for granted. This means that estimation errors are expected, and a good estimation algorithm should be able not only to compute estimates that are optimal in some sense, but also provide meaningful measures of uncertainty associated with those estimates. In some situations, we might also be able to reduce estimation uncertainty through the use of feedback on observations, an approach referred to as sensor management. Characterization of estimation uncertainty, as well as sensor management, are certainly difficult tasks for general partially observed processes, which might be non-linear, non-Gaussian, and/or have dependent process and observation noises. Sequential Monte Carlo (SMC) methods, also known as particle filters, are numerical Bayesian estimators which are, in principle, able to handle highly general estimation problems. However, SMC methods are known to suffer from a phenomenon called degeneracy, or self-resolving, which greatly impairs their usefulness against certain classes of problems. One of such classes, that we address in the first part of this thesis, is the joint state and parameter estimation problem, where there are unknown parameters to be estimated together with the timevarying state. Some SMC variants have been proposed to counter the degeneracy phenomenon for this problem, but these state-of-the-art techniques are either non-Bayesian or introduce biases on the system model, which might not be appropriate if proper characterization of estimation uncertainty is required. For this type of scenario, we propose using the Rao-Blackwellized Marginal Particle Filter (RBMPF), a combination of two SMC algorithm variants: the Rao-Blackwellized Particle Filter (RBPF) and the Marginal Particle Filter (MPF). We derive two new versions of the RBMPF: one for models with low dimensional parameter vectors, and another for more general models. We apply the proposed methods to two practical problems: the target tracking problem of turn rate estimation for a constant turn maneuver, and the econometrics problem of stochastic volatility estimation. Our proposed methods are shown to be effective solutions, both in terms of estimation accuracy and statistical consistency, i.e. characterization of estimation uncertainty. Another problem where standard particle filters suffer from degeneracy, addressed in the second part of this thesis, is the joint multi-target tracking and labelling problem. In comparison with the joint state and parameter estimation problem, this problem poses an additional challenge, namely, the fact that it has not been properly mathematically formulated in previous literature. Using Finite Set Statistics (FISST), we provide a sound theoretical formulation for the problem, and in order to actually solve the problem, we propose a novel Bayesian algorithm, the Labelling Uncertainty-Aware Particle Filter (LUA-PF) filter, essentially a combination of the RBMPF and the Multi-target Sequential Monte Carlo (M-SMC) filter techniques. We show that the new algorithm achieves significant improvements on both finding the correct track labelling and providing a meaningful measure of labelling uncertainty. In the last part of this thesis, we address the sensor management problem. Although we apply particle filters to the problem, they are not the main focus of this part of the work. Instead, we concentrate on a more fundamental question, namely, which sensor management criterion should be used in order to obtain the best results in terms of information gain and/or reduction of uncertainty. In order to answer this question, we perform an in-depth theoretical and empirical analysis on two popular sensor management criteria based on information theory – the Kullback-Leibler and R´enyi divergences. On the basis of this analysis, we are able to either confirm or reject some previous arguments used as theoretical justification for these two criteria

Novel methods for multi-target tracking with applications in sensor registration and fusion

Maintaining surveillance over vast volumes of space is an increasingly important capability for the defence industry. A clearer and more accurate picture of a surveillance region could be obtained through sensor fusion between a network of sensors. However, this accurate picture is dependent on the sensor registration being resolved. Any inaccuracies in sensor location or orientation can manifest themselves into the sensor measurements that are used in the fusion process, and lead to poor target tracking performance. Solutions previously proposed in the literature for the sensor registration problem have been based on a number of assumptions that do not always hold in practice, such as having a synchronous network and having small, static registration errors. This thesis will propose a number of solutions to resolving the sensor registration and sensor fusion problems jointly in an efficient manner. The assumptions made in previous works will be loosened or removed, making the solutions more applicable to problems that we are likely to see in practice. The proposed methods will be applied to both simulated data, and a segment of data taken from a live trial in the field