Finite mixture regression: a sparse variable selection by model selection for clustering.

Emilie Devijver (1, 2)

1 SELECT - Model selection in statistical learning
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

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.

Keywords: l1 regulariazed method.; l1 regulariazed method; Variable selection; finite mixture regression; non asymptotic penalized criterion

Domains: Statistics [math.ST]; Statistics Theory [stat.TH]

Emilie Devijver. Finite mixture regression: a sparse variable selection by model selection for clustering.. Electronic Journal of Statistics , 2015. ⟨hal-01060079⟩