Modelling sequential data is important in many areas of science and engineering. Hidden Markov models (HMMs) and Kalman filter models (KFMs) are popular for this because they are simple and flexible. For example, HMMs have been used for speech recognition and bio-sequence analysis, and KFMs have been used for problems ranging from tracking planes and missiles to predicting the economy. However, HMMs and KFMs are limited in their “expressive power”. Dynamic Bayesian Networks (DBNs) generalize HMMs by allowing the state space to be represented in factored form, instead of as a single discrete random variable. DBNs generalize KFMs by allowing arbitrary probability distributions, not just (unimodal) linear-Gaussian. In this thesis, I will discuss how to represent many different kinds of models as DBNs, how to perform exact and approximate inference in DBNs, and how to learn DBN models from sequential data. In particular, the main novel technical contributions of this thesis are as follows: a way of representing Hierarchical HMMs as DBNs, which enables inference to be done in O(T) time instead of O(T 3), where T is the length of the sequence; an exact smoothing algorithm that takes O(log T) space instead of O(T); a simple way of using the junction tree algorithm for online inference in DBNs; new complexity bounds on exact online inference in DBNs; a new deterministic approximate inference algorithm called factored frontier; an analysis of the relationship between the BK algorithm and loopy belief propagation; a way of applying Rao-Blackwellised particle filtering to DBNs in general, and the SLAM (simultaneous localization and mapping) problem in particular; a way of extending the structural EM algorithm to DBNs; and a variety of different applications of DBNs. However, perhaps the main value of the thesis is its catholic presentation of the field of sequential data modelling.

Machine Learning research has been making great progress in many directions. This article summarizes four of these directions and discusses some current open problems. The four directions are (a) improving classification accuracy by learning ensembles of classifiers, (b) methods for scaling up supervised learning algorithms, (c) reinforcement learning, and (d) learning complex stochastic models.

In this paper, we present a method for recognising an agent's behaviour in dynamic, noisy, uncertain domains, and across multiple levels of abstraction. We term this problem on-line plan recognition under uncertainty and view it generally as probabilistic inference on the stochastic process representing the execution of the agent's plan. Our contributions in this paper are twofold. In terms of probabilistic inference, we introduce the Abstract Hidden Markov Model (AHMM), a novel type of stochastic processes, provide its dynamic Bayesian network (DBN) structure and analyse the properties of this network. We then describe an application of the Rao-Blackwellised Particle Filter to the AHMM which allows us to construct an ecient, hybrid inference method for this model. In terms of plan recognition, we propose a novel plan recognition framework based on the AHMM as the plan execution model. The Rao-Blackwellised hybrid inference for AHMM can take advantage of the independence properties inherent in a model of plan execution, leading to an algorithm for online probabilistic plan recognition that scales well with the number of levels in the plan hierarchy. This illustrates that while stochastic models for plan execution can be complex, they exhibit special structures which, if exploited, can lead to efficient plan recognition algorithms. We demonstrate the usefulness of the AHMM framework via a behaviour recognition system in a complex spatial environment using distributed video surveillance data.

We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, thatrunsfora class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the Baum-Welch algorithm for HMMs, the Inside-Outside algorithm for PCFGs, and the one for singly connected Bayesian networks that have beendeveloped independently in each research eld. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can signi cantly outperform the Inside-Outside algorithm. 1.

Abstract — We extend lazy propagation for inference in single-agent Bayesian networks to multiagent lazy inference in multiply sectioned Bayesian networks (MSBNs). Two methods are proposed using distinct runtime structures. We prove that the new methods are exact and efficient when domain structure is sparse. Both improve space and time complexity than the existing method, which allow multiagent probabilistic reasoning to be performed in much larger domains given the computational resource. Relative performance of the three methods are compared analytically and experimentally. I.

Probabilistic models based on directed acyclic graphs have a long and rich tradition, beginning with work by the geneticist Sewall Wright in the 1920s. Variants have appeared in many fields. Within statistics, such models are known as directed graphical models; within cognitive science and artificial intelligence, such models are known as Bayesian networks.

In this paper we perform a comparison among FSS-EBNA, a randomized, populationbased and evolutionary algorithm, and two genetic and other two sequential search approaches in the well known Feature Subset Selection (FSS) problem. In FSS-EBNA, the FSS problem, stated as a search problem, uses the EBNA (Estimation of Bayesian Network Algorithm) search engine, an algorithm within the EDA (Estimation of Distribution Algorithm) approach. The EDA paradigm is born from the roots of the GA community in order to explicitly discover the relationships among the features of the problem and not disrupt them by genetic recombination operators. The EDA paradigm avoids the use of recombination operators and it guarantees the evolution of the population of solutions and the discovery of these relationships by the factorization of the probability distribution of best individuals in each generation of the search. In EBNA, this factorization is carried out by a Bayesian network induced by a chea...

Recently, variational approximations such as the mean field approximation have received much interest. We extend the standard mean field method by using an approximating distribution that factorises into cluster potentials. This includes undirected graphs, directed acyclic graphs and junction trees. We derive generalised mean field equations to optimise the cluster potentials. We show that the method bridges the gap between the standard mean field approximation and the exact junction tree algorithm. In addition, we address the problem of how to choose the structure and the free parameters of the approximating distribution. From the generalised mean field equations we derive rules to simplify the approximation in advance without affecting the potential accuracy of the model class. We also show how the method fits into some other variational approximations that are currently popular. 1 INTRODUCTION Graphical models, such as Bayesian networks, Markov fields, and Bolt...

Partially observable Markov decision processes (POMDPs) can be used to model complex control problems that include both action outcome uncertainty and imperfect observability. A control problem within the POMDP framework is expressed as a dynamic optimization problem with a value function that combines costs or rewards from multiple steps. Although the POMDP framework is more expressive than other simpler frameworks, like Markov decision processes (MDP), its associated optimization methods are more demanding computationally and only very small problems can be solved exactly in practice. Our work focuses on two possible approaches that can be used to solve larger problems: approximation methods and exploitation of additional problem structure. First, a number of new eÆcient approximation methods and improvements of existing algorithms are proposed. These include (1) the fast informed bound method based on approximate dynamic programming updates that lead to piecewise linear and convex v...

Abstract. In the last few years, there has been increasing interest from the agent community in the use of techniques from decision theory and game theory. Our aims in this article are firstly to briefly summarise the key concepts of decision theory and game theory, secondly to discuss how these tools are being applied in agent systems research, and finally to introduce this special issue of Autonomous Agents and Multi-Agent Systems by reviewing the papers that appear.