Hidden.Markov Models (HMMs) are applied t.0 the problems of statistical modeling, database searching and multiple sequence alignment of protein families and protein domains. These methods are demonstrated the on globin family, the protein kinase catalytic domain, and the EF-hand calcium binding motif. In each case the parameters of an HMM are estimated from a training set of unaligned sequences. After the HMM is built, it is used to obtain a multiple alignment of all the training sequences. It is also used to search the. SWISS-PROT 22 database for other sequences. that are members of the given protein family, or contain the given domain. The Hi " produces multiple alignments of good quality that agree closely with the alignments produced by programs that incorporate threedimensional structural information. When employed in discrimination tests (by examining how closely the sequences in a database fit the globin, kinase and EF-hand HMMs), the '\ HMM is able to distinguish members of these families from non-members with a high degree of accuracy. Both the HMM and PROFILESEARCH (a technique used to search for relationships between a protein sequence and multiply aligned sequences) perform better in these tests than PROSITE (a dictionary of sites and patterns in proteins). The HMM appecvs to have a slight advantage over PROFILESEARCH in terms of lower rates of false

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.

We survey the literature on methods for inference and learning in Bayesian Networks composed of discrete and continuous nodes, in which the continuous nodes have a multivariate Gaussian distribution, whose mean and variance depends on the values of the discrete nodes. We also briefly consider hybrid Dynamic Bayesian Networks, an extension of switching Kalman filters. This report is meant to summarize what is known at a sufficient level of detail to enable someone to implement the algorithms, but without dwelling on formalities.