  We consider a finite mixture of Gaussian regression model for high-
dimensional data, where the number of covariates may be much larger than the
sample size. We propose to estimate the unknown conditional mixture density by
a maximum likelihood estimator, restricted on relevant variables selected by an
1-penalized maximum likelihood estimator. We get an oracle inequality satisfied
by this estimator with a Jensen-Kullback-Leibler type loss. Our oracle
inequality is deduced from a general model selection theorem for maximum
likelihood estimators with a random model collection. We can derive the penalty
shape of the criterion, which depends on the complexity of the random model
collection.
