Uniform generalization errors in binary linear classification concentrate around their expectation at O(1/sqrt(n)) rates under unbounded Lipschitz losses, via new log-Sobolev inequalities for (Y_i X_i, Y_i).
Dimension-free uniform concentration bound for logistic regression
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We provide a novel dimension-free uniform concentration bound for the empirical risk function of constrained logistic regression. Our bound yields a milder sufficient condition for a uniform law of large numbers than conditions derived by the Rademacher complexity argument and McDiarmid's inequality. The derivation is based on the PAC-Bayes approach with second-order expansion and Rademacher-complexity-based bounds for the residual term of the expansion.
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Improved generalization bounds for binary linear classification via isoperimetry
Uniform generalization errors in binary linear classification concentrate around their expectation at O(1/sqrt(n)) rates under unbounded Lipschitz losses, via new log-Sobolev inequalities for (Y_i X_i, Y_i).