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Predictive Inference with Weak Supervision

Maxime Cauchois, Suyash Gupta, Alnur Ali, John C. Duchi; 25(118):1−45, 2024.


The expense of acquiring labels in large-scale statistical machine learning makes partially and weakly-labeled data attractive, though it is not always apparent how to leverage such data for model fitting or validation. We present a methodology to bridge the gap between partial supervision and validation, developing a conformal prediction framework to provide valid predictive confidence sets---sets that cover a true label with a prescribed probability, independent of the underlying distribution---using weakly labeled data. To do so, we introduce a (necessary) new notion of coverage and predictive validity, then develop several application scenarios, providing efficient algorithms for classification and several large-scale structured prediction problems. We corroborate the hypothesis that the new coverage definition allows for tighter and more informative (but valid) confidence sets through several experiments.

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