Abstract
We prove bounds on the population risk of the maximum margin algorithm for
two-class linear classification. For linearly separable training data, the
maximum margin algorithm has been shown in previous work to be equivalent to a
limit of training with logistic loss using gradient descent, as the training
error is driven to zero. We analyze this algorithm applied to random data
including misclassification noise. Our assumptions on the clean data include
the case in which the class-conditional distributions are standard normal
distributions. The misclassification noise may be chosen by an adversary,
subject to a limit on the fraction of corrupted labels. Our bounds show that,
with sufficient over-parameterization, the maximum margin algorithm trained on
noisy data can achieve nearly optimal population risk.
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