The Department of Statistics & OR will be holding a seminar entitled 'Regularization in Regression: Partial Least Squares and Constrained Maximum Likelihood Estimation' on Friday 3 May at 12:00 noon in Lab Room 602, Maths & Physics Building, University of Malta Msida Campus.

The speaker is Dr Monique Borg Inguanez.

Abstract

The need for regularization in the high-dimensional regression setting, where the number of explanatory variables rival or exceed the number of observations, is well established. Amongst the most famous regularization methods, which have been successfully applied in this setting, is the Partial Least Squares (PLS) method. The PLS estimation method can be regarded as estimation under a statistical model based on a 'Krylov hypothesis', which puts constraints on the joint covariance matrix. The resulting PLS estimator is not the maximum likelihood estimator but it can be calculated quickly using software and it has a closed form.  In this presentation we see how the PLS estimator can be modified to find the exact maximum likelihood (EML) estimate under the same model. The EML estimate is the solution to a constraint optimization problem that can be recast as an unconstrained optimization problem on the Grassmann manifold. 

Keywords: Regularization in Regression, PLS, Krylov Subspaces, Grassmann Optimization