Learning Dynamic Bayesian Networks

Suppose we wish to build a model of data from a finite sequence of ordered observations, . In most realistic scenarios, from modeling stock prices to physiological data, the observations are not related deterministically. Furthermore, there is added uncertainty resulting from the limited size of our data set and any mismatch between our model and the true process. Probability theory provides a powerful tool for expressing both randomness and uncertainty in our model [23]. We can express the uncertainty in our prediction of the future outcome Yt+1 via a probability density . Such a probability density can then be used to make point predictions, define error bars, or make decisions that are expected to minimize some loss function.This chapter presents a probabilistic framework for learning modelsof temporal data. We express these models using theBayesian network formalism (a.k.a. probabilistic graphical models orbelief networks) - a marriage of probability theory and graph theory inwhichdependencies between variables are expressed graphically. The graphnot only allows the user to understand which variables affect whichother ones, but also serves as the backbone for efficiently computingmarginal and conditional probabilities that may be required forinference and learning.The next section provides a brief tutorial of Bayesian networks.Section 3 demonstrates the use of Bayesian networksfor modeling time series, including some well-known examples such asthe Kalman filer and the hidden Markov model. Section 4 focuseson the problem of learning the parameters of a Bayesian network usingthe Expectation-Maximization (EM)algorithm [3, 10]. Section 5describes some richer models appropriate for time series withnonlinear or multiresolution structure. Inference in such models maybe computationally intractable. However, in section 6we present several tractable methods for approximate inference whichcan be used as the basis for learning.