Inference for High-dimensional Single-Index Models

Preprint on Arxiv: https://arxiv.org/abs/1909.03540

In this project we developed methods for constructing confidence intervals and hypothesis tests for the linear component of high-dimensional single-index models. Single-index models generalize linear models by allowing the reponse $y$ to depend on a non-linear function of a linear combination of the predictors: $$y=g(⟨x,\beta ⟩)$$ This can avoid curse of dimensionality because we are not dealing with a fully non-parametric model $y=g(x)$ which suffers from curse of dimensionality. Even for a high-dimensional $\beta$, we still estimate $\beta$ if it is sparse and the design is elliptically symmetric.

The code for experiments in the paper is available on github: https://github.com/ehamid/sim_debiasing