B0537
Title: SuperMix: Sparse regularization for mixtures
Authors: Clement Marteau - Université Lyon 1 (France) [presenting]
Abstract: The statistical estimation of a discrete mixing measure $\mu^0$ involved in a kernel mixture model is investigated. Using some recent advances in $l_1$-regularization over the space of measures, we introduce a data fitting and regularization convex program for estimating $\mu^0$ in a grid-less manner from a sample of mixture law, this method is referred to as Beurling-LASSO. We derive a lower bound on the bandwidth of our data fitting term depending only on the support of $\mu^0$ and its so-called minimum separation to ensure quantitative support localization error bounds. Under a so-called non-degenerate source condition, we derive a non-asymptotic support stability property. This latter shows that for a sufficiently large sample size $n$, our estimator has exactly as many weighted Dirac masses as the target~$\mu^0$, converging in amplitude and localization towards the true ones. Statistical performances of this estimator are investigated designing a so-called dual certificate, which is appropriate to our setting. The classical Gaussian distribution will be discussed.
