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.

A new method is proposed for exploiting causal independencies in exact Bayesian network inference.

The theory of belief networks offers a relatively new approach for dealing with uncertain information in knowledge-based (expert) systems. In contrast with the heuristic techniques for reasoning with uncertainty employed in many rule-based expert systems, the theory of belief networks is mathematically sound, based on techniques from probability theory. It therefore seems attractive to convert existing rule-based expert systems into belief networks. In this article, we discuss the design of a belief network reformulation of the diagnostic rule-based expert system HEPAR. For the purpose of this experiment, we have studied several typical pieces of medical knowledge represented in the HEPAR system. It turned out that, due to the differences in the type of knowledge represented and in the formalism used to represent uncertainty, much of the medical knowledge required for building the belief network concerned could not be extracted from HEPAR. As a consequence, significant additional knowledge acquisition was required. However, the objects and attributes defined in the HEPAR system, as well as the conditions in production rules mentioning these objects and attributes were useful for guiding the selection of the statistical variables for building the belief network. The mapping of objects and attributes in HEPAR to statistical variables is discussed in detail.

The problem of achieving small total state space for triangulated belief graphs (networks) is considered. It is an NP-complete problem to find a triangulation with minimum state space. Our interest

In this paper we present a method for decomposition of Bayesian networks into their maximal prime subgraphs. The correctness of the method is proven and results relating the maximal prime subgraph decomposition to the maximal complete subgraphs of the moral graph of the original Bayesian network are presented. The maximal prime subgraphs of a Bayesian network can be organized as a tree which can be used as the computational structure for lazy propagation. We have also identified a number of tasks performed on Bayesian networks that can benefit from maximal prime subgraph decomposition. These tasks include divide and conquer triangulation, hybrid propagation algorithms combining exact and approximative inference techniques, and incremental construction of junction trees. Finally, we present the results of a series empirical evaluations relating the accumulated number of variables in maximal prime subgraphs of equal size to the size of the maximal prime subgraphs. 1 1

Probabilistic networks are now fairly well established as practical representations of knowledge for reasoning under uncertainty, as demonstrated by an increasing number of successful applications in such domains as (medical) diagnosis and prognosis, planning, vision,

An extension of the expert system shell HUGIN to include continuous wriables, in the form of linear additive normally distributed variables, is presented. The

Reasoning in Bayesian networks is exponential in a graph parameter w3 known as induced width (also known as tree-width and max-clique size). In this paper, we investigate the potential of causal independence (CI) for improving this performance. We consider several tasks, such as belief updating, nding a most probable explanation (MPE), nding a maximum aposteriori hypothesis (MAP), and nding the maximum expected utility (MEU). We show that exploiting CI in belief updating can signi cantly reduce the e ective w3, sometimes down to the induced width of the unmoralized network's graph. For example, for poly-trees, CI reduces complexity from exponential to linear in the family size. Similar results hold for the MAP and MEU tasks, while the MPE task is less sensitive to CI. These enhancements are incorporated into bucket-elimination algorithms based on known approaches of network transformations [10, 13] and elimination [18]. We provide an ordering heuristic which guarantees that exploiting CI will never hurt the performance. Finally, wediscuss an e cient wayof propagating evidence in CI-networks using arc-consistency, and apply this idea to noisy-OR networks. The resulting algorithm generalizes the Quickscore algorithm [9] for BN2O networks. 1

Sensitivity analysis is a method to investigate the effects of varying a model's parameters on its predictions. It was recently suggested as a suitable means to facilitate quantifying the joint probability distribution of a Bayesian belief network. This article presents practical experience with performing sensitivity analyses on a belief network in the field of medical prognosis and treatment planning. Three network quantifications with different levels of informedness were constructed. Two poorly-informed quantifications were improved by replacing the most influential parameters with the corresponding parameter estimates from the well-informed network quantification; these influential parameters were found by performing one-way sensitivity analyses. Subsequently, the results of the replacements were investigated by comparing network predictions. It was found that it may be sufficient to gather a limited number of highly-informed network parameters to obtain a satisfying network quant...

This paper investigates the applicability of a Monte Carlo technique known as `simulated annealing' to achieve optimum or sub-optimum decompositions of probabilistic networks under bounded resources. High-quality decompositions are essential for performing efficient inference in probabilistic networks. Optimum decomposition of probabilistic networks is known to be NP-hard (Wen 1990). The paper proves that cost-function changes can be computed locally, which is essential to the efficiency of the annealing algorithm. Pragmatic control schedules which reduce the running time of the annealing algorithm are presented and evaluated. Apart from the conventional temperature parameter, these schedules involve the radius of the search space as a new control parameter. The evaluation suggests that the inclusion of this new parameter is important for the success of the annealing algorithm for the present problem.