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D. Kapla:
"Fusing Sufficient Dimension Reduction with Neural Networks";
Talk: Statistics seminar, University of Jyväskylä, Finnland (online); 2021-12-03.

We consider the regression problem where the dependence of the response Y on a set of predictors X is fully captured by the regression function E(Y | X) = g(B'X), for an unknown function g and low rank parameter B matrix. We combine neural networks with sufficient dimension reduction in order to remove the limitation of small data sets. We show in simulations that the proposed estimator is on par with competing sufficient dimension reduction methods, such as minimum average variance estimation and conditional variance estimation, in small data sets. Its main advantage is its scalability in regressions for large data sets, for which the other methods are infeasible.