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We develop methods for estimating Fr\'echet bounds on (possiblyhigh-dimensional) distribution classes in which some variables arecontinuous-valued. We establish the statistical correctness of the computedbounds under uncertainty in the marginal constraints and demonstrate theusefulness of our algorithms by evaluating the performance of machine learning(ML) models trained with programmatic weak supervision (PWS). PWS is aframework for principled learning from weak supervision inputs (e.g.,crowdsourced labels, knowledge bases, pre-trained models on related tasks,etc), and it has achieved remarkable success in many areas of science andengineering. Unfortunately, it is generally difficult to validate theperformance of ML models trained with PWS due to the absence of labeled data.Our algorithms address this issue by estimating sharp lower and upper boundsfor performance metrics such as accuracy/recall/precision/F1 score.

Estimating Fr\'echet bounds for validating programmatic weak supervision