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.

Bayesiannetworks provide a languagefor qualitatively representing the conditional independence properties of a distribution. This allows a natural and compact representation of the distribution, eases knowledge acquisition, and supports effective inference algorithms.

. We examine a novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks. Our approach explicitly represents and learns the local structure in the conditional probability distributions (CPDs) that quantify these networks. This increases the space of possible models, enabling the representation of CPDs with a variable number of parameters. The resulting learning procedure induces models that better emulate the interactions present in the data. We describe the theoretical foundations and practical aspects of learning local structures and provide an empirical evaluation of the proposed learning procedure. This evaluation indicates that learning curves characterizing this procedure converge faster, in the number of training instances, than those of the standard procedure, which ignores the local structure of the CPDs. Our results also show that networks learned with local structures tend to be more complex (in terms of a...

The Bayes Net Toolbox (BNT) is an open-source Matlab package for directed graphical models. BNT supports many kinds of nodes (probability distributions), exact and approximate inference, parameter and structure learning, and static and dynamic models. BNT is widely used in teaching and research: the web page has received over 28,000 hits since May 2000. In this paper, we discuss a broad spectrum of issues related to graphical models (directed and undirected), and describe, at a high-level, how BNT was designed to cope with them all. We also compare BNT to other software packages for graphical models, and to the nascent OpenBayes effort.

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

Recently, there has been much interest in reverse engineering genetic networks from time series data. In this paper, we show that most of the proposed discrete time models — including the boolean network model [Kau93, SS96], the linear model of D’haeseleer et al. [DWFS99], and the nonlinear model of Weaver et al. [WWS99] — are all special cases of a general class of models called Dynamic Bayesian Networks (DBNs). The advantages of DBNs include the ability to model stochasticity, to incorporate prior knowledge, and to handle hidden variables and missing data in a principled way. This paper provides a review of techniques for learning DBNs. Keywords: Genetic networks, boolean networks, Bayesian networks, neural networks, reverse engineering, machine learning. 1

We define a language for representing context-sensitive probabilistic knowledge. A knowledge base consists of a set of universally quantified probability sentences that include context constraints, which allow inference to be focused on only the relevant portions of the probabilistic knowledge. We provide a declarative semantics for our language. We present a query answering procedure which takes a query Q and a set of evidence E and constructs a Bayesian network to compute P (QjE). The posterior probability is then computed using any of a number of Bayesian network inference algorithms. We use the declarative semantics to prove the query procedure sound and complete. We use concepts from logic programming to justify our approach. Keywords: reasoning under uncertainty, Bayesian networks, Probability model construction, logic programming Submitted to Theoretical Computer Science special issue on Uncertainty in Databases and Deductive Systems. This work was partially supported by NSF g...

Stochastic sampling algorithms, while an attractive alternative to exact algorithms in very large Bayesian network models, have been observed to perform poorly in evidential reasoning with extremely unlikely evidence. To address this problem, we propose an adaptive importance sampling algorithm, AIS-BN, that shows promising convergence rates even under extreme conditions and seems to outperform the existing sampling algorithms consistently. Three sources of this performance improvement are (1) two heuristics for initialization of the importance function that are based on the theoretical properties of importance sampling in nite-dimensional integrals and the structural advantages of Bayesian networks, (2) a smooth learning method for the importance function, and (3) a dynamic weighting function for combining samples from dierent stages of the algorithm. We tested the performance of the AIS-BN algorithm along with two state of the art general purpose sampling algorithms, lik...

Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are introduced and (2) the impact of a single cause on the effect does not depend on what other causes have previously been applied. In this paper, we introduce an equivalent atemporal characterization of causal independence based on a functional representation of the relationship between causes and the effect. In this representation, the interaction between causes and effect can be written as a nested decomposition of functions. Causal independence can be exploited by representing this decomposition in the belief network, resulting in representations that are more efficient for inference than general causal models. We present empirical results showing the benefits of a causal-independence representation for belief-network inference. 1

ABayesian network is a probabilistic representation for uncertain relationships, which has proven to be useful for modeling real-world problems. When there are many potential causes of a given e ect, however, both probability assessment and inference using a Bayesian network can be di cult. In this paper, we describe causal independence, a collection of conditional independence assertions and functional relationships that are often appropriate to apply to the representation of the uncertain interactions between causes and e ect. We show how the use of causal independence in a Bayesian network can greatly simplify probability assessment aswell as probabilistic inference. 1