Hidden Markov Decision Trees
Michael I. Jordan, Zoubin Ghahramani, Lawrence K. Saul · Cambridge University Engineering Department Publications Database · 1996
We study a time series model that can be viewed as a decision tree with Markov temporal structure. The model is intractable for exact calculations, thus we utilize variational approximations. We consider three different distributions for the approximation: one in which the Markov calculations are performed exactly and the layers of the decision tree are decoupled, one in which the decision tree calculations are performed exactly and the time steps of the Markov chain are decoupled, and one in which a Viterbi-like assumption is made to pick out a single most likely state sequence. We present simulation results for artificial data and the Bach chorales. Accepted for oral presentation at NIPS*96. 1 Introduction Decision trees are regression or classification models that are based on a nested decomposition of the input space. An input vector x is classified recursively by a set of "decisions" at the nonterminal nodes of a tree, resulting in the choice of a terminal node at which an output...