ABSTRACT
Dynamic Bayesian Networks:
Representation, Inference and Learning
by
Kevin Patrick Murphy
Doctor of Philosophy in Computer Science
University of California, Berkeley
Professor Stuart Russell, Chair
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.
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