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In this technical report, we consider conditional density estimation with amaximum likelihood approach. Under weak assumptions, we obtain a theoreticalbound for a Kullback-Leibler type loss for a single model maximum likelihoodestimate. We use a penalized model selection technique to select a best modelwithin a collection. We give a general condition on penalty choice that leadsto oracle type inequality for the resulting estimate. This construction isapplied to two examples of partition-based conditional density models, modelsin which the conditional density depends only in a piecewise manner from thecovariate. The first example relies on classical piecewise polynomial densitieswhile the second uses Gaussian mixtures with varying mixing proportion but samemixture components. We show how this last case is related to an unsupervisedsegmentation application that has been the source of our motivation to thisstudy.

Conditional Density Estimation by Penalized Likelihood Model Selection and Applications