Padhraic Smyth wrote: > One of the most useful developments (from my own viewpoint > at least) has been the realization that one can treat a HMM > as a type of belief network - in fact once one does this one > sees immediately that it is in fact a relatively *simple* model, i.e., > > x_1 -- x_2 --...... -- x_T > | | | > | | | > y_1 y_2 y_T > > where here the x's are the hidden states and y's are the observed > variables, and the directionality of the edges is usually assumed > to be from x_t to x_t+1 and from x_t to y_t. Yes, I've found this view of HMMs very useful in my work in speech recognition. Bayesian networks are *very* useful as a conceptual tool. When I draw a Bayesian network, it's not because I want to input it to Netica or Hugin or whatever and evaluate it on some data; it's because I want to construct a probabilistic model of some problem, or better understand an existing one, so that I can derive recognition and/or training algorithms from the model. With a Bayesian network in hand, it's easy to keep track of what conditional independencies I can use; without one, it's very easy to mistakenly assume that two quantities are conditionally independent when they are not. -- Kevin S. Van Horn
