dc.contributor.author Deng, Zeyu dc.contributor.author Kammoun, Abla dc.contributor.author Thrampoulidis, Christos dc.date.accessioned 2019-12-23T12:10:20Z dc.date.available 2019-12-23T12:10:20Z dc.date.issued 2019-11-13 dc.identifier.uri http://hdl.handle.net/10754/660756 dc.description.abstract We consider a model for logistic regression where only a subset of features of size $p$ is used for training a linear classifier over $n$ training samples. The classifier is obtained by running gradient-descent (GD) on the logistic-loss. For this model, we investigate the dependence of the generalization error on the overparameterization ratio $\kappa=p/n$. First, building on known deterministic results on convergence properties of the GD, we uncover a phase-transition phenomenon for the case of Gaussian regressors: the generalization error of GD is the same as that of the maximum-likelihood (ML) solution when $\kappa<\kappa_\star$, and that of the max-margin (SVM) solution when $\kappa>\kappa_\star$. Next, using the convex Gaussian min-max theorem (CGMT), we sharply characterize the performance of both the ML and SVM solutions. Combining these results, we obtain curves that explicitly characterize the generalization error of GD for varying values of $\kappa$. The numerical results validate the theoretical predictions and unveil double-descent phenomena that complement similar recent observations in linear regression settings. dc.publisher arXiv dc.relation.url https://arxiv.org/pdf/1911.05822 dc.rights Archived with thanks to arXiv dc.title A Model of Double Descent for High-dimensional Binary Linear Classification dc.type Preprint dc.contributor.department Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division dc.eprint.version Pre-print dc.contributor.institution Electrical and Computer Engineering Department at the University of California, Santa Barbara, USA dc.identifier.arxivid 1911.05822 kaust.person Kammoun, Abla refterms.dateFOA 2019-12-23T12:10:51Z
﻿

### Files in this item

Name:
Preprintfile1.pdf
Size:
452.7Kb
Format:
PDF
Description:
Pre-print