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In this paper, we develop data-dependent and algorithm-dependentgeneralization bounds for transductive learning algorithms in the context ofinformation theory for the first time. We show that the generalization gap oftransductive learning algorithms can be bounded by the mutual informationbetween training labels and hypothesis. By innovatively proposing the conceptof transductive supersamples, we go beyond the inductive learning setting andestablish upper bounds in terms of various information measures. Furthermore,we derive novel PAC-Bayesian bounds and build the connection betweengeneralization and loss landscape flatness under the transductive learningsetting. Finally, we present the upper bounds for adaptive optimizationalgorithms and demonstrate the applications of results on semi-supervisedlearning and graph learning scenarios. Our theoretic results are validated onboth synthetic and real-world datasets.

Information-Theoretic Generalization Bounds for Transductive Learning and its Applications