# Jeremie HoussineauThe University of Warwick · Department of Statistics

Jeremie Houssineau

PhD

## About

65

Publications

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655

Citations

Introduction

Additional affiliations

June 2011 - December 2015

September 2009 - March 2011

## Publications

Publications (65)

We propose a general solution to the problem of robust Bayesian inference in complex settings where outliers may be present. In practice, the automation of robust Bayesian analyses is important in the many applications involving large and complex datasets. The proposed solution relies on a reformulation of Bayesian inference based on possibility th...

This paper presents a flexible modeling framework for multi-target tracking based on the theory of Outer Probability Measures (OPMs). The notion of labeled uncertain finite set is introduced and utilized as the basis to derive a possibilistic analog of the $\delta$ -Generalized Labeled Multi-Bernoulli ( $\delta$ -GLMB) filter, in which the uncertai...

Bearings-only tracking using passive sensors is important for covert surveillance of moving targets. This paper adopts a mathematical formulation of bearings-only tracking in the framework of possibility theory, where uncertainties are represented using possibility functions, rather than usual probability distributions. Possibility functions have t...

A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted observations. In order to account for the lack of information about the different aspects of this type of com...

We consider the problem of statistical inference for a class of partially-observed diffusion processes, with discretely-observed data and finite-dimensional parameters. We construct unbiased estimators of the score function, i.e. the gradient of the log-likelihood function with respect to parameters, with no time-discretization bias. These estimato...

We present a modelling framework for multi-target tracking based on possibility theory and illustrate its ability to account for the general lack of knowledge that the target-tracking practitioner must deal with when working with real data. We also introduce and study variants of the notions of point process and intensity function, which lead to th...

A novel solution to the smoothing problem for multi-object dynamical systems is proposed and evaluated. The systems of interest contain an unknown and varying number of dynamical objects that are partially observed under noisy and corrupted observations. An alternative representation of uncertainty is considered in order to account for the lack of...

The Bernoulli filter is a Bayes filter for joint detection and tracking of a target in the presence of false and miss detections. This paper presents a mathematical formulation of the Bernoulli filter in the framework of possibility theory, where uncertainty is represented using possibility functions, rather than probability distributions. Possibil...

The basis of this short introduction is a review of the literature on communicating uncertainty, with a particular focus on visualising uncertainty. From our review, one thing emerges very clearly: there is no ‘optimal’ format or framework for visualising uncertainty. Instead, the implementation of visualisation techniques must be studied on a case...

The Bernoulli filter is a Bayes filter for joint detection and tracking of a target in the presence of false and miss detections. This paper presents a mathematical formulation of the Bernoulli filter in the framework of possibility theory, where uncertainty is represented using {\em possibility} functions, rather than {\em probability} distributio...

Outer measures can be used for statistical inference in place of probability measures to bring flexibility in terms of model specification. The corresponding statistical procedures such as estimation or hypothesis testing need to be analysed in order to understand their behaviour, and motivate their use. In this article, we consider a simple class...

This paper presents the filter for Hypothesised and Independent Stochastic Populations (HISP), a multi-object joint detection/tracking algorithm derived from a recent estimation framework for stochastic populations, in the context of Space Situational Awareness. Designed for multi-object estimation problems where the data association between tracks...

Bearings-only target motion analysis (TMA) is the process of estimating the state of a moving emitting target from noisy measurements collected by a single passive observer. The focus of this study is on recursive TMA, traditionally solved using the Bayesian filters (e.g. extended or unscented Kalman filters, particle filters). The TMA is a difficu...

This work considers a target tracking problem where the observed information is in the form of natural language-type statements. More specifically, the focus is on a spatio-temporal tracking problem where each uttered expression may involve both spatial, motion and temporal uncertainty, and a general modelling framework for natural language stateme...

The problem is target motion analysis (TMA), where the objective is to estimate the state of a moving target from noise corrupted bearings-only measurements. The focus is on recursive TMA, traditionally solved using the Bayesian filters (e.g. the extended or unscented Kalman filters, particle filters). The TMA is a difficult problem and may cause t...

In this article we consider the smoothing problem for hidden Markov models (HMM). Given a hidden Markov chain $\{X_n\}_{n\geq 0}$ and observations $\{Y_n\}_{n\geq 0}$, our objective is to compute $\mathbb{E}[\varphi(X_0,\dots,X_k)|y_{0},\dots,y_n]$ for some real-valued, integrable functional $\varphi$ and $k$ fixed, $k \ll n$ and for some realisati...

The concept of Fisher information can be useful even in cases where the probability distributions of interest are not absolutely continuous with respect to the natural reference measure on the underlying space. Practical examples where this extension is useful are provided in the context of multi-object tracking statistical models. Upon defining th...

Maintaining a catalog of Resident Space Objects (RSOs) can be cast in a typical Bayesian multi-object estimation problem, where the various sources of uncertainty in the problem - the orbital mechanics, the kinematic states of the identified objects, the data sources, etc. - are modeled as random variables with associated probability distributions....

A recent trend in distributed multi-sensor fusion is to use random finite set filters at the sensor nodes and fuse the filtered distributions algorithmically using their exponential mixture densities (EMDs). Fusion algorithms which extend the celebrated covariance intersection and consensus based approaches are such examples. In this article, we an...

We explore the interplay between random and deterministic phenomena using a novel representation of uncertainty. The proposed framework strengthens the connections between the frequentist and Bayesian approaches by allowing for the two viewpoints to coexist within a unified formulation. The meaning of the analogues of different probabilistic concep...

In real environments, it is seldom that physical dynamical systems can be observed without detection failures and without disturbances from the background. Yet, a vast majority of the literature regarding Bayesian inference for such systems ignore these undesired effects and assume that pre-processing can be applied to remove them. To some extent,...

In this article we consider recursive approximations of the smoothing distribution associated to partially observed stochastic differential equations (SDEs), which are observed discretely in time. Such models appear in a wide variety of applications including econometrics, finance and engineering. This problem is notoriously challenging, as the smo...

Closed-form stochastic filtering and smoothing recursions can be derived for a specific class of outer measures. In this article, we study how the principles of the sequential Monte Carlo method can be adapted for the purpose of practical implementation of these recursions. In particular, we explore how sampling can be used to provide support point...

Surveillance activities with ground-based assets in the context of space situational awareness are particularly challenging. The observation process is indeed hindered by short observation arcs, limited observability, missed detections, measurement noise, and contamination by clutter. This paper exploits a recent estimation framework for stochastic...

Learning the model parameters of a multi-object dynamical system from partial and perturbed observations is a challenging task. Despite recent numerical advancements in learning these parameters, theoretical guarantees are extremely scarce. In this article, we study the identifiability of these parameters and the consistency of the corresponding ma...

The Probability Hypothesis Density (PHD) and Cardinalized PHD (CPHD) filters are popular solutions to the multi-target tracking problem due to their low complexity and ability to estimate the number and states of targets in cluttered environments. The PHD filter propagates the first-order moment (i.e. mean) of the number of targets while the CPHD p...

Filtering and smoothing with a generalised representation of uncertainty is considered. Here, uncertainty is represented using a class of outer measures. It is shown how this representation of uncertainty can be propagated using outer-measure-type versions of Markov kernels and generalised Bayesian-like update equations. This leads to a system of g...

The computation of expectations w.r.t. probability laws associated to a discretization are found in a wide variety of applications, for instance in applied mathematics. We consider the scenario where the discretization is in multiple dimensions, for instance for stochastic partial differential equations (SPDEs), where discretization is in space and...

To circumvent the intractability of the usual Cardinalized Probability Hypothesis Density (CPHD) smoother, we present an approximate scheme where the population of targets born until and after the starting time of the smoothing are estimated separately and where smoothing is only applied to the estimate of the former population. The approach is ill...

A multi-target filtering algorithm is introduced based on recent works on the modelling of partially-distinguishable populations and on the representation of partial information. This framework enables practically-relevant aspects of multi-target systems to be modelled and embedded in a principled way, such as pre-existing knowledge about the popul...

A flexible representation of uncertainty that remains within the standard framework of probabilistic measure theory is presented along with a study of its properties. This representation relies on a specific type of outer measure that is based on the measure of a supremum, hence combining additive and highly sub-additive components. It is shown tha...

In its classical form, the cardinalized probability hypothesis density (CPHD) filter does not model the appearance of new targets through spawning, yet there are applications for which spawning models more appropriately account for newborn objects when compared to spontaneous birth models. In this paper, we propose a principled derivation of the CP...

A way of representing heterogeneous stochastic populations that are composed of sub-populations with different levels of distinguishability is introduced together with an analysis of its properties. In particular, it is demonstrated that any instance of this representation where individuals are independent can be related to a point process on the s...

Multiple-input multiple-output (MIMO) sonar systems offer new perspectives for area surveillance especially in complex environments where strong multipath and dense clutter can become very challenging. This study proposes a MIMO sonar system based scheme to tackle the difficult problem of harbour surveillance. An emphasis is put on recognition and...

In the last decade, the area of multiple target tracking has witnessed the introduction of important concepts and methods, aiming at establishing principled approaches for dealing with the estimation of multiple objects in an efficient way. One of the most successful classes of multi-object filters that have been derived out of these new grounds in...

In environments of scarce hygiene it is of primary importance to detect potentially harmful concentrations of pathogens in drinking water. In many situations, however, accurate analysis of water samples is prohibitively complex and often requires highly specialised apparatuses and technicians. In order to overcome these limitations, a method to emp...

This paper investigates a sensor management scheme that aims at minimising the regional variance in the number of objects present in regions of interest whilst performing multi-target filtering with the PHD filter. The experiments are conducted in a simulated environment with groups of targets moving through a scene in order to inspect the behaviou...

A formulation of the hypothesised filter for independent stochastic populations (hisp) is proposed, based on the concept of association measure, which is a measure on the set of observation histories. Using this formulation, a particle approximation is introduced at the level of the association measure for handling the exponential growth in the num...

In the classical derivation, the CPHD (Cardinalized Probability Hypothesis
Density) filter does not model the appearance of new targets through spawning.
However, there are applications for which spawning models more appropriately
account for new targets than birth models, with the caveat that they may create
issues with computational tractability....

This paper summarizes the core definitions and results regarding the chain
differential for functions in locally convex topological vector spaces. In
addition, it provides a few elementary calculus rules of practical interest,
notably for the differentiation of characteristic functionals in various
domains of physical science and engineering.

Calibrating multiple cameras is a fundamental prerequisite for many Computer Vision applications. Typically this involves using a pair of identical synchronized industrial or high-end consumer cameras. This paper considers an application on a pair of low-cost portable cameras with different parameters that are found in smart phones. This paper addr...

The SC-PHD filter is an algorithm which was designed to solve a class of multiple object estimation problems where it is necessary to estimate the state of a single-target parent process, in addition to estimating the state of a multi-object population which is conditioned on it. The filtering process usually employs a number of particles to repres...

For many disciplines in natural sciences like biology, chemistry or medicine, the invention of optical microscopy in the late 1800's provided groundbreaking insight into biomedical mechanisms that were not observable before with the unaided eye. However, the diffraction limit of the microscope gives a natural constraint on the image resolution sinc...

This article introduces a multi-object filter for the resolution of joint
detection/tracking problems involving multiple targets, derived from the novel
Bayesian estimation framework for stochastic populations. Fully probabilistic
in nature, the filter for Distinguishable and Independent Stochastic
Populations (DISP) exploits two exclusive probabil...

Fluorescence microscopy is a technique which allows the imaging of cellular and intracellular dynamics through the activation of fluorescent molecules attached to them. It is a very important technique because it can be used to analyze the behavior of intracellular processes in vivo in contrast to methods like electron microscopy. There are several...

Methods for sensor control are crucial for modern surveillance and sensing systems to enable efficient allocation and prioritisation of resources. The framework of partially observed Markov decision processes enables decisions to be made based on data received by the sensors within an information-theoretic context. This work addresses the problem o...

Object triangulation, 3-D object tracking, feature correspondence, and camera
calibration are key problems for estimation from camera networks. This paper
addresses these problems within a unified Bayesian framework for joint
multi-object tracking and sensor registration. Given that using standard
filtering approaches for state estimation from came...

Recent generalisations of stochastic filtering methods to multi-object systems have become very popular for solving multi-target tracking problems over the last decade. However, there was previously no general means of introducing correlations between objects. In this article, we investigate generalisations of such multi-object filters for systems...

Volterra series are used for modelling nonlinear systems with memory effects. The nth-order impulse response and the kernels in the series can be determined with Fréchet derivatives of Volterra series operators. Consequently, we can determine the kernels of composite systems by taking higher-order Fréchet derivatives of composite series. The genera...

In the context of multi-target tracking application, the concept of variance in the number of targets estimated in specified regions of the surveillance scene has been recently introduced for multi-object filters. This article has two main objectives. First, the regional variance is derived for a multi-object representation commonly used in the tra...

This short paper focuses on the structure of the data association problem and details a solution based on the introduction of distinguishability in the representation of a given stochastic population. This approach allows for the derivation of general filtering equations for independent stochastic populations. Based on these general equations, the...

The probability generating functional (p.g.fl.) provides a useful means of compactly representing point process models. Cluster processes can be described through the composition of p.g.fl.s, and factorial moment measures and Janossy measures can be recovered from the p.g.fl. using variational derivatives. This article describes the application of...

Photoactivated Localization Microscopy (PALM) is a technique which allows the localization of particles smaller than the resolution of the microscope and can be used to analyze intracellular particle motion. Images acquired with this technique, however, are noisy, which complicates particle detection, and tracking the particles is complicated due t...

This paper determines the general formula for describing differentials of
composite functions in terms of differentials of their factor functions. This
generalises the formula commonly attributed to Faa di Bruno to functions in
locally convex topological vector spaces. The result highlights the general
structure of the higher-order chain rule in te...

Recent progress in multi-object filtering has led to algorithms that compute
the first-order moment of multi-object distributions based on sensor
measurements. The number of targets in arbitrarily selected regions can be
estimated using the first-order moment. In this work, we introduce explicit
formulae for the computation of the second-order stat...

This document contains the notes of some of the lectures given at the first
summer school on Finite Set Statistics held in Edinburgh from July 22, 2013 to
July 26, 2013. The notes are mostly self contained and are accessible to
everyone.

Mahler’s Probability Hypothesis Density (PHD filter), proposed in 2000, addresses the challenges of the multipletarget
detection and tracking problem by propagating a mean density of the targets in any region of the state
space. However, when retrieving some local evidence on the target presence becomes a critical component of
a larger process - e....

The problem of estimating interacting systems of multiple objects is
important to a number of different fields of mathematics, physics, and
engineering. Drawing from a range of disciplines, including statistical
physics, variational calculus, point process theory, and statistical sensor
fusion, we develop a unified probabilistic framework for model...

Estimating the position of an object from cameras is a key requirement in many computer vision and robotics applications. In sensor fusion applications, where we integrate data from multiple observations and cameras over time and estimate the uncertainty in the state estimate, a Bayesian approach is more applicable than the usual Maximum Likelihood...

This paper presents a simple and efficient way to set the birth process of the Probability Hypothesis Density filter that enhances the performance of this approach when tracking multiple targets in clutter with no a priori spatial information on where targets can appear. The novelty introduced concerns the intensity of the birth Random Finite Set t...

This paper considers the challenging problem of multitarget tracking with passive data, obtained here by geographically distributed cameras. We use a Gaussian Mixture Probability Hypothesis Density filter approach to solve this difficult problem. As we make no spatial assumptions for the birth process, we use a slightly modified filter to obtain ou...

## Projects

Projects (3)

(Completed project) Explore the possibilities and understand the limitations of the finite set statistics framework

Propose flexible solutions to problems involving the estimation of multiple individuals through noisy and incomplete observations corrupted by false possitives and detection failures.

Derive filtering and smoothing algorihtms as well as the corresponding computable approximations for a specific class of outer measures based on functional integration of the supremum.