10 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…
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…
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 $…
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…
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…
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…