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Label noise in data has long been an important problem in supervised learning applications as it affects the effectiveness of many widely used classification methods. Recently, important real-world applications, such as medical diagnosis and cybersecurity, have generated renewed interest in the Neyman-Pearson (NP) classification paradigm, which constrains the more severe type of error (e.g., the type I error) under a preferred level while minimizing the other (e.g., the type II error). However, there has been little research on the NP paradigm under label noise. It is somewhat surprising that even when common NP classifiers ignore the label noise in the training stage, they are still able to control the type I error with high probability. However, the price they pay is excessive conservativeness of the type I error and hence a significant drop in power (i.e., $1 - $ type II error). Assuming that domain experts provide lower bounds on the corruption severity, we propose the first theory-backed algorithm that adapts most state-of-the-art classification methods to the training label noise under the NP paradigm. The resulting classifiers not only control the type I error with high probability under the desired level but also improve power.

We investigate the fairness issue in classification, where automated decisions are made for individuals from different protected groups. In high-consequence scenarios, decision errors can disproportionately affect certain protected groups, leading to unfair outcomes. To address this issue, we propose a fairness-adjusted selective inference (FASI) framework and develop data-driven algorithms that achieve statistical parity by controlling the false selection rate (FSR) among protected groups. Our FASI algorithm operates by converting the outputs of black-box classifiers into R-values, which are both intuitive and computationally efficient. These R-values serve as the basis for selection rules that are provably valid for FSR control in finite samples for protected groups, effectively mitigating the unfairness in group-wise error rates. We demonstrate the numerical performance of our approach using both simulated and real data.

We consider the common setting where one observes probability estimates for a large number of events, such as default risks for numerous bonds. Unfortunately, even with unbiased estimates, selecting events corresponding to the most extreme probabilities can result in systematically underestimating the true level of uncertainty. We develop an empirical Bayes approach "Excess Certainty Adjusted Probabilities" (ECAP), using a variant of Tweedie's formula, which updates probability estimates to correct for selection bias. ECAP is a flexible non-parametric method, which directly estimates the score function associated with the probability estimates, so it does not need to make any restrictive assumptions about the prior on the true probabilities. ECAP also works well in settings where the probability estimates are biased. We demonstrate through theoretical results, simulations, and an analysis of two real world data sets, that ECAP can provide significant improvements over the original probability estimates.