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Tight Sample Complexity of Large-Margin Learning
Sivan Sabato · Nati Srebro · Naftali Tishby

Wed Dec 08 12:00 AM -- 12:00 AM (PST) @

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L2 regularization: We introduce the gamma-adapted-dimension, which is a simple function of the spectrum of a distribution's covariance matrix, and show distribution-specific upper and lower bounds on the sample complexity, both governed by the gamma-adapted-dimension of the source distribution. We conclude that this new quantity tightly characterizes the true sample complexity of large-margin classification. The bounds hold for a rich family of sub-Gaussian distributions.

Author Information

Sivan Sabato (Ben-Gurion University of the Negev)
Nati Srebro (TTI-Chicago)
Naftali Tishby (The Hebrew University Jerusalem)

Naftali Tishby, is a professor of computer science and the director of the Interdisciplinary Center for Neural Computation (ICNC) at the Hebrew university of Jerusalem. He received his Ph.D. in theoretical physics from the Hebrew University and was a research staff member at MIT and Bell Labs from 1985 to 1991. He was also a visiting professor at Princeton NECI, the University of Pennsylvania and the University of California at Santa Barbara. Dr. Tishby is a leader of machine learning research and computational neuroscience. He was among the first to introduce methods from statistical physics into learning theory, and dynamical systems techniques in speech processing. His current research is at the interface between computer science, statistical physics and computational neuroscience and concerns the foundations of biological information processing and the connections between dynamics and information.

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