1 code implementation • 1 Apr 2024 • Pratik Patil, Jin-Hong Du, Ryan J. Tibshirani
We study the behavior of optimal ridge regularization and optimal ridge risk for out-of-distribution prediction, where the test distribution deviates arbitrarily from the train distribution.
no code implementations • 26 Feb 2024 • Pratik Patil, Yuchen Wu, Ryan J. Tibshirani
We analyze the statistical properties of generalized cross-validation (GCV) and leave-one-out cross-validation (LOOCV) applied to early-stopped gradient descent (GD) in high-dimensional least squares regression.
1 code implementation • 6 Oct 2023 • Pratik Patil, Daniel LeJeune
We also propose an "ensemble trick" whereby the risk for unsketched ridge regression can be efficiently estimated via GCV using small sketched ridge ensembles.
1 code implementation • 2 Oct 2023 • Pierre C. Bellec, Jin-Hong Du, Takuya Koriyama, Pratik Patil, Kai Tan
We provide a non-asymptotic analysis of the CGCV and the two intermediate risk estimators for ensembles of convex penalized estimators under Gaussian features and a linear response model.
1 code implementation • 1 Jun 2023 • Riccardo Fogliato, Pratik Patil, Pietro Perona
Matching algorithms are commonly used to predict matches between items in a collection.
no code implementations • 25 Apr 2023 • Jin-Hong Du, Pratik Patil, Arun Kumar Kuchibhotla
We study subsampling-based ridge ensembles in the proportional asymptotics regime, where the feature size grows proportionally with the sample size such that their ratio converges to a constant.
no code implementations • 27 Feb 2023 • Jin-Hong Du, Pratik Patil, Kathryn Roeder, Arun Kumar Kuchibhotla
By establishing uniform consistency of our risk extrapolation technique over ensemble and subsample sizes, we show that ECV yields $\delta$-optimal (with respect to the oracle-tuned risk) ensembles for squared prediction risk.
no code implementations • 20 Oct 2022 • Pratik Patil, Jin-Hong Du, Arun Kumar Kuchibhotla
Bagging is a commonly used ensemble technique in statistics and machine learning to improve the performance of prediction procedures.
no code implementations • 25 May 2022 • Pratik Patil, Arun Kumar Kuchibhotla, Yuting Wei, Alessandro Rinaldo
Recent empirical and theoretical analyses of several commonly used prediction procedures reveal a peculiar risk behavior in high dimensions, referred to as double/multiple descent, in which the asymptotic risk is a non-monotonic function of the limiting aspect ratio of the number of features or parameters to the sample size.