Statistical inference of time-dependent data

Probabilistic graphical modeling is a framework which can be used to succinctly
represent multivariate probability distributions of time series in terms of each time
series’s dependence on others. In general, it is computationally prohibitive to sta-
tistically infer an arbitrary model from data. However, if we constrain the model to
have a tree topology, the corresponding learning algorithms become tractable. The
expressive power of tree-structured distributions are low, since only n − 1 dependen-
cies are explicitly encoded for an n node tree. One way to improve the expressive
power of tree models is to combine many of them in a mixture model. This work
presents and uses simulations to validate extensions of the standard mixtures of trees
model for i.i.d data to the setting of time series data. We also consider the setting
where the tree mixture itself forms a hidden Markov chain, which could be better
suited for approximating time-varying seasonal data in the real world. Both of these
are evaluated on artificial data sets.