Dear All,

We have the pleasure thanks to the support of the ESSEC IDS dpt, Institut des Actuaires, LabEx MME-DII, the group BFA (SFdS), to invite you to the seminar by:

We study the problem of regularised maximum-likelihood optimisation in ill-posed generalised linear models with covariates that include subsets that are relevant and that are irrelevant for the response. It is assumed that the source of ill-posedness is a joint low dimensionality of the response and a subset of the relevant covariates in the sense of a latent factor generalised linear model (GLM). In particular, we propose a novel iteratively reweighted partial least squares (IRPLS) algorithm and show that it is better than any other projection or penalisation based regularisation method. Under regularity assumptions on the latent factor GLM we show that the convergence rate of the IRPLS estimator with high probability is the same as that of the maximum likelihood estimator in our latent factor GLM, which is an oracle achieving an optimal parametric rate. Our findings are confirmed by numerical studies.