Statistical-Computational Tradeoff in Single Index Models

Authors: Lingxiao Wang, Zhuoran Yang, Zhaoran Wang

NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Theoretical We study the statistical-computational tradeoffs in a high dimensional single index model Y = f(X β ) + ϵ, where f is unknown, X is a Gaussian vector and β is s-sparse with unit norm. ... Using the statistical query model to characterize the computational cost of an algorithm, we show that when Cov(Y, X β ) = 0 and Cov(Y, (X β )2) > 0, no computationally tractable algorithms can achieve the information-theoretic limit of the minimax risk. This implies that one must pay an extra computational cost for the nonlinearity involved in the model.
Researcher Affiliation Academia Northwestern University; lingxiaowang2022@u.northwestern.edu Princeton University; zy6@princeton.edu Northwestern University; zhaoranwang@gmail.com
Pseudocode No The paper does not include any pseudocode or clearly labeled algorithm blocks.
Open Source Code No The paper does not provide any concrete access to source code for the methodology described.
Open Datasets No The paper is theoretical and does not describe experiments with datasets, thus no training data information is provided.
Dataset Splits No The paper is theoretical and does not describe experiments with datasets, thus no validation split information is provided.
Hardware Specification No The paper is theoretical and does not describe any experiments that would require hardware specifications.
Software Dependencies No The paper is theoretical and does not describe any software implementation details or dependencies with version numbers.
Experiment Setup No The paper is theoretical and does not describe any experimental setup details such as hyperparameters or training settings.