1 citations · 2 across the 11 of their papers we have counts for
12 papers
Generalization Error Estimation for Primal--Dual Algorithms in Non-Smooth Regression
Kai Tan, Pierre C Bellec
This paper studies trajectory-wise estimation of generalization error for primal--dual algorithms in non-smooth regression. Motivating examples include \(\ell_1\)-penalized least a…
The Lasso error is bounded iff its active set size is bounded away from n in the proportional regime
Pierre C. Bellec
This note develops an analysis of the Lasso \( \hat b\) in linear models without any sparsity or L1 assumption on the true regression vector, in the proportional regime where dimen…
Phase transitions for the existence of unregularized M-estimators in single index models
Takuya Koriyama, Pierre C. Bellec
This paper studies phase transitions for the existence of unregularized M-estimators under proportional asymptotics where the sample size and feature dimension grow proport…
Simultaneous analysis of approximate leave-one-out cross-validation and mean-field inference
Pierre C Bellec
Approximate Leave-One-Out Cross-Validation (ALO-CV) is a method that has been proposed to estimate the generalization error of a regularized estimator in the high-dimensional regim…
Optimizing over iid distributions and the Beat the Average game
Pierre C Bellec, Tobias Fritz
A casino offers the following game. There are three cups each containing a die. You are being told that the dice in the cups are all the same, but possibly nonstandard. For a bet o…
Estimating Generalization Performance Along the Trajectory of Proximal SGD in Robust Regression
Kai Tan, Pierre C. Bellec
This paper studies the generalization performance of iterates obtained by Gradient Descent (GD), Stochastic Gradient Descent (SGD) and their proximal variants in high-dimensional r…
Precise Asymptotics of Bagging Regularized M-estimators
Takuya Koriyama, Pratik Patil, Jin-Hong Du +2
We characterize the squared prediction risk of ensemble estimators obtained through subagging (subsample bootstrap aggregating) regularized M-estimators and construct a consistent…
Uncertainty quantification for iterative algorithms in linear models with application to early stopping
Pierre C. Bellec, Kai Tan
This paper investigates the iterates $\hbb^1,\dots,\hbb^T$ obtained from iterative algorithms in high-dimensional linear regression problems, in the regime where the feature dimens…
Asymptotics of resampling without replacement in robust and logistic regression
Pierre C. Bellec, Takuya Koriyama
This paper studies the asymptotics of resampling without replacement in the proportional regime where dimension and sample size are of the same order. For a given dataset $…
Error estimation and adaptive tuning for unregularized robust M-estimator
Pierre C. Bellec, Takuya Koriyama
We consider unregularized robust M-estimators for linear models under Gaussian design and heavy-tailed noise, in the proportional asymptotics regime where the sample size n and the…
Existence of solutions to the nonlinear equations characterizing the precise error of M-estimators
Pierre C. Bellec, Takuya Koriyama
Major progress has been made in the previous decade to characterize the asymptotic behavior of regularized M-estimators in high-dimensional regression problems in the proportional…
Corrected generalized cross-validation for finite ensembles of penalized estimators
Pierre C. Bellec, Jin-Hong Du, Takuya Koriyama +2
Generalized cross-validation (GCV) is a widely-used method for estimating the squared out-of-sample prediction risk that employs a scalar degrees of freedom adjustment (in a multip…