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- W4306816001 abstract "We provide an exact characterization of the expected generalization error (gen-error) for semi-supervised learning (SSL) with pseudo-labeling via the Gibbs algorithm. The gen-error is expressed in terms of the symmetrized KL information between the output hypothesis, the pseudo-labeled dataset, and the labeled dataset. Distribution-free upper and lower bounds on the gen-error can also be obtained. Our findings offer new insights that the generalization performance of SSL with pseudo-labeling is affected not only by the information between the output hypothesis and input training data but also by the information {em shared} between the {em labeled} and {em pseudo-labeled} data samples. This serves as a guideline to choose an appropriate pseudo-labeling method from a given family of methods. To deepen our understanding, we further explore two examples -- mean estimation and logistic regression. In particular, we analyze how the ratio of the number of unlabeled to labeled data $lambda$ affects the gen-error under both scenarios. As $lambda$ increases, the gen-error for mean estimation decreases and then saturates at a value larger than when all the samples are labeled, and the gap can be quantified {em exactly} with our analysis, and is dependent on the emph{cross-covariance} between the labeled and pseudo-labeled data samples. For logistic regression, the gen-error and the variance component of the excess risk also decrease as $lambda$ increases." @default.
- W4306816001 created "2022-10-20" @default.
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- W4306816001 date "2022-10-15" @default.
- W4306816001 modified "2023-09-25" @default.
- W4306816001 title "How Does Pseudo-Labeling Affect the Generalization Error of the Semi-Supervised Gibbs Algorithm?" @default.
- W4306816001 doi "https://doi.org/10.48550/arxiv.2210.08188" @default.
- W4306816001 hasPublicationYear "2022" @default.
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