Synthetic-Powered Multiple Testing with FDR Control

Multiple hypothesis testing with false discovery rate (FDR) control is a fundamental problem in statistical inference, with broad applications in genomics, drug screening, and outlier detection. In many such settings, researchers may have access not only to real experimental observations but also to auxiliary or synthetic data -- from past, related experiments or generated by generative models -- that can provide additional evidence about the hypotheses of interest. We introduce SynthBH, a synthetic-powered multiple testing procedure that safely leverages such synthetic data. We prove that SynthBH guarantees finite-sample, distribution-free FDR control under a mild PRDS-type positive dependence condition, without requiring the pooled-data p-values to be valid under the null. The proposed method adapts to the (unknown) quality of the synthetic data: it enhances the sample efficiency and may boost the power when synthetic data are of high quality, while controlling the FDR at a user-specified level regardless of their quality. We demonstrate the empirical performance of SynthBH on tabular outlier detection benchmarks and on genomic analyses of drug-cancer sensitivity associations, and further study its properties through controlled experiments on simulated data.

Synthetic-Powered Predictive Inference

Conformal prediction is a framework for predictive inference with a distribution-free, finite-sample guarantee. However, it tends to provide uninformative prediction sets when calibration data are scarce. This paper introduces Synthetic-powered predictive inference (SPPI), a novel framework that incorporates synthetic data -- e.g., from a generative model -- to improve sample efficiency. At the core of our method is a score transporter: an empirical quantile mapping that aligns nonconformity scores from trusted, real data with those from synthetic data. By carefully integrating the score transporter into the calibration process, SPPI provably achieves finite-sample coverage guarantees without making any assumptions about the real and synthetic data distributions. When the score distributions are well aligned, SPPI yields substantially tighter and more informative prediction sets than standard conformal prediction. Experiments on image classification and tabular regression demonstrate notable improvements in predictive efficiency in data-scarce settings.

Binary classification with corrupted labels

In a binary classification problem where the goal is to fit an accurate predictor, the presence of corrupted labels in the training data set may create an additional challenge. However, in settings where likelihood maximization is poorly behaved-for example, if positive and negative labels are perfectly separable-then a small fraction of corrupted labels can improve performance by ensuring robustness. In this work, we establish that in such settings, corruption acts as a form of regularization, and we compute precise upper bounds on estimation error in the presence of corruptions. Our results suggest that the presence of corrupted data points is beneficial only up to a small fraction of the total sample, scaling with the square root of the sample size.