Matthieu Marbac - Model Selection for Non-Parametric Multivariate Finite Mixture Models

This talk addresses the problems of model estimation for finite mixture models within a non-parametric framework. In particular, we are interested in methods that provide consistent estimators of the model, as well as methods that allow for the validation of the estimated model on the data.
In the first part, we consider the specific case of bivariate data to introduce methods that rely on integral operators. We show that these methods can be used to select the number of components in a mixture model and the number of states in a hidden Markov model. 
In the second part, the dimension of the random vector is left unrestricted, and we present an approach for selecting the number of components and the subset of discriminative variables. This approach involves a discretization of each variable into a number of bins that grows with the sample size and a penalization of the resulting log-likelihood.
In the final part, we present a goodness-of-fit procedure that validates the model-based clustering outputs.
This talk is based on joint works with Marie Du Roy, Salima El Kolei and Mohammed Sedki