Exact Distribution Of Statistics Of Hidden State Sequences Via Message Passing in Factor Graphs Available to Purchase

We compute exact distributions of statistics of hidden state sequences through the sum‐product algorithm defined over cycle‐free factor graphs. Matrix operators are included to sequentially update a vector that indicates the statistic value corresponding to sums of products of evaluated potential functions. The methodology may be used for both undirected and directed models, with applications to discrete hidden state sequences perturbed by noise and/or missing values, and state sequences that serve to classify observations. Examples are given to illustrate the computational procedure.