03.12.2018 14:00 Timo Klock:
Adaptively estimating nonlinear single index models with monotonic link functionsMI 02.10.011 (Boltzmannstr. 3, 85748 Garching)
The single index model (SIM) is a popular tool for modeling data where the output depends on the features through a linear 1D projection. If data follows this model, efficient estimation at 1D minimax rates is possible. However, the model space is restricted by the assumed linearity. In this talk we introduce a generalized SIM that allows for projections onto 1D manifolds. We propose an estimator based on local linear regression, where the localization happens in the output domain instead of in the feature domain. Finally, we present theoretical guarantees and numerical studies on real data sets to support the usefulness of a nonlinear SIM.