2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information

2021 IEEE International Conference on Acoustics, Speech and Signal Processing

6-11 June 2021 • Toronto, Ontario, Canada

Extracting Knowledge from Information
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Paper Detail

Paper IDMLSP-45.5
Paper Title BENIGN OVERFITTING IN BINARY CLASSIFICATION OF GAUSSIAN MIXTURES
Authors Ke Wang, University of California, Santa Barbara, United States; Christos Thrampoulidis, University of British Columbia, Canada
SessionMLSP-45: Performance Bounds
LocationGather.Town
Session Time:Friday, 11 June, 13:00 - 13:45
Presentation Time:Friday, 11 June, 13:00 - 13:45
Presentation Poster
Topic Machine Learning for Signal Processing: [MLR-PERF] Bounds on performance
IEEE Xplore Open Preview  Click here to view in IEEE Xplore
Abstract Deep neural networks generalize well despite being exceedingly overparameterized, but understanding the statistical principles behind this so called benign-overfitting phenomenon is not yet well understood. Recently there has been remarkable progress towards understanding benign-overfitting in simpler models, such as linear regression and, even more recently, linear classification. This paper studies benign-overfitting for data generated from a popular binary Gaussian mixtures model (GMM) and classifiers trained by support-vector machines (SVM). Our approach has two steps. First, we leverage an idea introduced in [Muthukumar et al. 2020] to relate the SVM solution to the least-squares (LS) solution. Second, we derive novel non-asymptotic bounds on the test error of LS solution. Combining the two gives sufficient conditions on the overparameterization ratio and the signal-to-noise ratio that lead to benign overfitting. We corroborate our theoretical findings with numerical simulations.