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# Tight Bounds for the Expected Risk of Linear Classifiers and PAC-Bayes Finite-Sample Guarantees

*Proceedings of the Seventeenth International Conference on Artificial Intelligence and Statistics*, PMLR 33:384-392, 2014.

#### Abstract

We analyze the expected risk of linear classifiers for a fixed weight vector in the “minimax” setting. That is, we analyze the worst-case risk among all data distributions with a given mean and covariance. We provide a simpler proof of the tight polynomial-tail bound for general random variables. For sub-Gaussian random variables, we derive a novel tight exponential-tail bound. We also provide new PAC-Bayes finite-sample guarantees when training data is available. Our “minimax” generalization bounds are dimensionality-independent and \mathcalO(\sqrt1/m) for m samples.