[tech] graphical models

sounds like a sexy name, doesn't it? well it's a sexy subject: the combination of probability theory and graph theory (you wish you were taking the class, don't you!).

in all seriousness, this class looks like it's going to be about really interesting tools for modelling complex systems. probability theory and statistics are all the rage now in computer science, and so i'm glad i have a pretty good background in those areas.

a way of thinking about this subject is to consider a graph where the nodes are random variables, and the edges between those nodes represent some sort of dependency between the random variables. probably the simplest example of such a model is a markov chain. you remember these: the outcome of step i+1 was only dependent on what occurred at step i. here's a drawing:

Xi -----> Xi+1 -------> Xi+2

notice this is a simple graph, with the Xs as nodes. the directed edge between Xi and Xi+1 indicates the relationship between the two random variables. Now imagine more complicated graphs, and imagine hidden nodes whose behavior we don't understand but must be inferred. fascinating!