The Benjamini-Hochberg (BH) procedure is widely used to control the false detection rate (FDR) in multiple testing.

Instead, we apply powerful machine learning models for one-class (Moya et al., 1993) or

Controlling the false discovery rate (FDR) in high-dimensional variable selection requires balancing rigorous error control with statistical power. Existing methods with provable guarantees are often overly conservative, creating a persistent gap between the realized false discovery proportion (FDP) and the target FDR level. We introduce a learning-augmented enhancement of the T-Rex Selector framework that narrows this gap. Our approach replaces the analytical FDP estimator with a neural network trained solely on diverse synthetic datasets, enabling a substantially tighter and more accurate approximation of the FDP. This refinement allows the procedure to operate much closer to the desired FDR level, thereby increasing discovery power while maintaining effective approximate control. Through extensive simulations and a challenging synthetic genome-wide association study (GWAS), we demonstrate that our method achieves superior detection of true variables compared to existing approaches.

Identifying truly predictive covariates while strictly controlling false discoveries remains a fundamental challenge in nonlinear, highly correlated, and low signal-to-noise regimes, where deep learning based feature selection methods are most attractive. We propose Group Regularization Importance Persistence in 2 Dimensions (GRIP2), a deep knockoff feature importance statistic that integrates first-layer feature activity over a two-dimensional regularization surface controlling both sparsity strength and sparsification geometry. To approximate this surface integral in a single training run, we introduce efficient block-stochastic sampling, which aggregates feature activity magnitudes across diverse regularization regimes along the optimization trajectory. The resulting statistics are antisymmetric by construction, ensuring finite-sample FDR control. In extensive experiments on synthetic and semi-real data, GRIP2 demonstrates improved robustness to feature correlation and noise level: in high correlation and low signal-to-noise ratio regimes where standard deep learning based feature selectors may struggle, our method retains high power and stability. Finally, on real-world HIV drug resistance data, GRIP2 recovers known resistance-associated mutations with power better than established linear baselines, confirming its reliability in practice.

Conformal inference provides a general distribution-free method to rigorously calibrate the output of any machine learning algorithm for novelty detection. While this approach has many strengths, it has the limitation of being randomized, in the sense that it may lead to different results when analyzing twice the same data and this can hinder the interpretation of any findings. We propose to make conformal inferences more stable by leveraging suitable conformal e-values instead of p-values to quantify statistical significance. This solution allows the evidence gathered from multiple analyses of the same data to be aggregated effectively while provably controlling the false discovery rate. Further, we show that the proposed method can reduce randomness without much loss of power compared to standard conformal inference, partly thanks to an innovative way of weighting conformal e-values based on additional side information carefully extracted from the same data. Simulations with synthetic and real data confirm this solution can be effective at eliminating random noise in the inferences obtained with state-of-the-art alternative techniques, sometimes also leading to higher power.

In bandit multiple hypothesis testing, each arm corresponds to a different null hypothesis that we wish to test, and the goal is to design adaptive algorithms that correctly identify large set of interesting arms (true discoveries), while only mistakenly identifying a few uninteresting ones (false discoveries). One common metric in non-bandit multiple testing is the false discovery rate (FDR). We propose a unified, modular framework for bandit FDR control that emphasizes the decoupling of exploration and summarization of evidence. We utilize the powerful martingale-based concept of e-processes to ensure FDR control for arbitrary composite nulls, exploration rules and stopping times in generic problem settings. In particular, valid FDR control holds even if the reward distributions of the arms could be dependent, multiple arms may be queried simultaneously, and multiple (cooperating or competing) agents may be querying arms, covering combinatorial semi-bandit type settings as well. Prior work has considered in great detail the setting where each arm's reward distribution is independent and sub-Gaussian, and a single arm is queried at each step. Our framework recovers matching sample complexity guarantees in this special case, and performs comparably or better in practice. For other settings, sample complexities will depend on the finer details of the problem (composite nulls being tested, exploration algorithm, data dependence structure, stopping rule) and we do not explore these; our contribution is to show that the FDR guarantee is clean and entirely agnostic to these details.