2019/11/13 by Zeyu Deng, Deng, Zeyu, Abla Kammoun +3 · 3 citations
Computer Science · Engineering · Mathematics · #FOS: Computer and information sciences #FOS: Electrical engineering #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Machine Learning and Algorithms #Signal Processing (eess.SP) #Sparse and Compressive Sensing Techniques #Statistical Methods and Inference #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1911.05822
openalex publication_date 2019/11/13 · openalex created_date 2019/11/22 · openalex updated_date 2026/07/28
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 logistic loss. For this model, we investigate the dependence of the classification error on the overparameterization ratio κ=p/n. First, building on known deterministic results on the implicit bias of GD, we uncover a phase-transition phenomenon for the case of Gaussian features: the classification error of GD is the same as that of the maximum-likelihood (ML) solution when κκ_⋆. Next, using the convex Gaussian min-max theorem (CGMT), we sharply characterize the performance of both the ML and the SVM solutions. Combining these results, we obtain curves that explicitly characterize the classification error for varying values of κ. The numerical results validate the theoretical predictions and unveil double-descent phenomena that complement similar recent findings in linear regression settings as well as empirical observations in more complex learning scenarios.