Improved Risk Bounds with Unbounded Losses for Transductive Learning
Keywords: concentration inequality, generalization bounds, graph neural networks, transductive learning, unbounded losses
TL;DR: We derive two novel concentration inequalities for suprema of empirical processes when sampled without replacement for unbounded functions, which take the variance of the functions into consideration and apply our new inequalities to GNNs.
Abstract: In the transductive learning setting, we are provided with a labeled training set and an unlabeled test set, with the objective of predicting the labels of the test points. This framework differs from the standard problem of fitting an unknown distribution with a training set drawn independently from this distribution. In this paper, we primarily improve the generalization bounds in transductive learning. Specifically, we develop two novel concentration inequalities for the suprema of empirical processes sampled without replacement for unbounded functions, marking the first discussion of the generalization performance of unbounded functions in the context of sampling without replacement. We further provide two valuable applications of our new inequalities: on one hand, we firstly derive fast excess risk bounds for empirical risk minimization in transductive learning under unbounded losses. On the other hand, we establish high-probability bounds on the generalization error for graph neural networks when using stochastic gradient descent which improve the current state-of-the-art results.
Primary Area: learning theory
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Submission Number: 14106
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