Tatyana Krivobokova - University of Vienna

"Iterative regularisation methods for ill-posed generalised linear models"

Abstract

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 algorithm. 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.

Additional information:

  • Speaker: Tatyana Krivobokova
  • Time: Thursday, 26.01.2023, 15:15 - 16:15
  • Location: Faculty Lounge, Room 0.036
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  • Organizer: Statistics Group
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