Title: Extending Sufficient Dimension Reduction to Regressions with Categorical
       Predictors

Speaker: Francesca Chiaromonte
	 Penn State University

Abstract:

As high-dimensional data sets become increasingly common, sufficient
dimension reduction provides a theoretical foundation and effective
methodology for the low-dimensional management of regressions involving a
large number of quantitative predictors. In many applications, though,
quantitative predictors, to be reduced through linear combinations, come
together with qualitative predictors. In this talk, we lay down the
theoretical basis of partial dimension reduction, in which the sufficient
reduction of a set of quantitative predictor is filtered through a
subpopulation structure generated by categorical variables. We also
describe how one of the most popular dimension reduction methods, sliced
inverse regression (SIR), can be adapted to partial reduction under
appropriate assumptions. Finally, we present some applications.