Search Results for author: Pratik Patil

Found 9 papers, 4 papers with code

Optimal Ridge Regularization for Out-of-Distribution Prediction

1 code implementation1 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.

regression

Failures and Successes of Cross-Validation for Early-Stopped Gradient Descent

no code implementations26 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.

Prediction Intervals regression

Asymptotically free sketched ridge ensembles: Risks, cross-validation, and tuning

1 code implementation6 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.

Prediction Intervals regression

Corrected generalized cross-validation for finite ensembles of penalized estimators

1 code implementation2 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.

Subsample Ridge Ensembles: Equivalences and Generalized Cross-Validation

no code implementations25 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.

Extrapolated cross-validation for randomized ensembles

no code implementations27 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.

Bagging in overparameterized learning: Risk characterization and risk monotonization

no code implementations20 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.

Mitigating multiple descents: A model-agnostic framework for risk monotonization

no code implementations25 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.

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