Mohit Sharma, Okan Koç, Amit Deshpande, Takashi Ishida, Gang Niu, Rajiv Ratn Shah, Masashi Sugiyama
There is a fundamental limit to the best prediction error of any model for a given data distribution. In classification, the Bayes error quantifies this limit and serves as both a benchmark for trained models and a criterion to detect overfitting. The state-of-the-art Bayes error estimation techniques for binary classification use only soft labels (positive class probabilities) and require no input features or auxiliary training. We extend such notions to constrained classification problems, such as fairness. Fair classification is an important case of constrained or multi-objective classification. It requires a model not only to be accurate but also to yield fair outcomes (equal or near-equal true positive rates) across different demographic groups (e.g., race and gender). This leads to an inherent fairness-accuracy tradeoff or a Pareto frontier that is used to compare fair classifiers against each other. The focus of our work is to estimate the fundamental limit for this fairness-accuracy tradeoff. We derive an explicit expression for the fair Bayes error rate (i.e., best achievable error rate subject to given fairness constraints), and construct consistent, instance-free estimators for it using only soft labels and group information. We provably bound the bias and the sample complexity of our estimators. Empirically, our method produces a robust, low-variance estimate of the optimal fairness-accuracy tradeoff curve, even when the soft labels are noisy and derived from a classification model on hard labels.
Large language models and text-to-speech technology enable low-cost production of dialogue-based lessons: videos in which two speakers converse. The speakers' roles can vary, but little is known about whether all learners respond alike to such differences. In a repeated-measures design, 222 first-year high school students viewed lessons in three formats: a teacher and a student (TS), two students (SS), and two teachers (TT). Within the aptitude-treatment interaction framework, linear mixed-effects models tested whether associations between learner characteristics and outcomes differed by format. The learner characteristics were experiential learning style - seeking challenging, new experiences (CE factor) and learning by reflecting on experience (RCE factor) - and critical thinking disposition; the outcomes were motivation based on the ARCS model, self-reported learning outcomes, and overall evaluation. For motivation, both factors interacted with format: the CE factor's association differed between TS and TT, and the RCE factor's slope was significantly positive in TS and SS and significantly larger in TS than TT. For learning outcomes, no interaction was detected, but critical thinking disposition was positively associated with them. For overall evaluation, again no interaction was detected, but TT was rated lowest. Given small-to-medium interaction effects, these findings are preliminary evidence to inform personalized learning design.
Multicalibration requires predicted scores to agree with label probabilities across rich families of subgroups and score-dependent tests, but existing methods require clean input-label pairs for evaluation and post-processing. This assumption fails in weakly supervised learning (WSL) regimes -- including positive-unlabeled, unlabeled-unlabeled, and positive-confidence learning -- where clean labels are costly or unavailable even though reliable uncertainty estimates may be crucial. We address this gap by developing estimators of multicalibration error and post-hoc correction methods for WSL settings in which clean input-label pairs are unavailable. We propose a unified framework for estimating and correcting multicalibration under weak supervision by combining contamination-matrix risk rewrites with witness-based calibration constraints, yielding corrected multicalibration moments with finite-sample guarantees. We further propose weak-label multicalibration boost (WLMC), a generic post-hoc recalibration algorithm under weak supervision. Finally, we conduct experiments across multiple weak-supervision settings to evaluate multicalibration behavior and offer empirical insight into uncertainty estimation under weak supervision.