An E-M algorithm for joint model estimation

In the unlabeled data problem, data contains signals from various sources whose identities are not known apriori, yet the parameters of the individual sources must be estimated. To do this optimally, it is necessary to optimize the data PDE which may be modeled as a mixture density, jointly over the parameters of all the signal models. This can present a problem of enormous complexity if the number of signal classes is large. This paper describes a algorithm for jointly estimating the parameters of the various signal types, each with different parameterizations and associated sufficient statistics. In doing so, it maximizes the likelihood function of all the parameters jointly, but does so without incurring the full dimensionality of the problem. It allows lower-dimensional sufficient statistics to be utilized for each signal model, yet still achieves joint optimality. It uses an extension of the class-specific decomposition of the Bayes minimum error probability classifier.