Using Inside-Outside Algorithm for Estimation of the Offspring Distribution in Multitype Branching Processes
Keywords:Multitype Branching Processes, Offspring Distribution, Maximum Likelihood Estimation, Expectation Maximization, Stochastic Context-Free Grammars, Inside-Outside Algorithm
Multitype branching processes (MTBP) model branching structures, where the nodes of the resulting tree are particles of different types. Usually such a process is not observable in the sense of the whole tree, but only as the “generation” at a given moment in time, which consists of the number of particles of every type. This requires an EM-type algorithm to obtain a maximum likelihood (ML) estimate of the parameters of the branching process. Using a version of the inside-outside algorithm for stochastic context-free grammars (SCFG), such an estimate could be obtained for the offspring distribution of the process.