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Simultaneous Monitoring of Shape and Surface Color via 4D Point Clouds: A Registration-free Approach When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Functional-prior-based approaches to Bayesian PDE-constrained inversion using physics-informed neural networks Optimal Experiments for Partial Causal Effect Identification Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? How Low-Precision Drives Slingshot Loss Spikes Tuning Derivatives for Causal Fairness in Machine Learning Spherical Flows for Sampling Categorical Data Bayesian Rain Field Reconstruction using Commercial Microwave Links and Diffusion Model Priors GRALIS: A Unified Canonical Framework for Linear Attribution Methods via Riesz Representation Sharp Capacity Thresholds in Linear Associative Memory: From Winner-Take-All to Listwise Retrieval Unified Framework of Distributional Regret in Multi-Armed Bandits and Reinforcement Learning Jacobian-Velocity Bounds for Deployment Risk Under Covariate Drift Self-Attention as Transport: Limits of Symmetric Spectral Diagnostics Perturbation is All You Need for Extrapolating Language Models Adapt or Forget: Provable Tradeoffs Between Adam and SGD in Nonstationary Optimization Realizable Bayes-Consistency for General Metric Losses Graph Convolutional Support Vector Regression for Robust Spatiotemporal Forecasting of Urban Air Pollution Segmenting Human-LLM Co-authored Text via Change Point Detection Stochastic Schrödinger Diffusion Models for Pure-State Ensemble Generation Understanding Self-Supervised Learning via Latent Distribution Matching The Geometric Mechanics of Contrastive Representation Learning: Alignment Potentials, Entropic Dispersion, and Cross-modal Divergence Imbalanced Classification under Capacity Constraints On the Spectral Structure and Objective Equivalence of Orthogonal Multilabel Fisher Discriminants Partially Observed Structural Causal Models
Beyond Fixed False Discovery Rates: Post-Hoc Conformal Se...
Meiyi Zhu, Osvaldo Simeone · 2026-04-13 · via stat updates on arXiv.org

Conformal selection (CS) uses calibration data to identify test inputs whose unobserved outcomes are likely to satisfy a pre-specified minimal quality requirement, while controlling the false discovery rate (FDR). Existing methods fix the target FDR level before observing data, which prevents the user from adapting the balance between number of selected test inputs and FDR to downstream needs and constraints based on the available data. For example, in genomics or neuroimaging, researchers often inspect the distribution of test statistics, and decide how aggressively to pursue candidates based on observed evidence strength and available follow-up resources. To address this limitation, we introduce {post-hoc CS} (PH-CS), which generates a path of candidate selection sets, each paired with a data-driven false discovery proportion (FDP) estimate. PH-CS lets the user select any operating point on this path by maximizing a user-specified utility, arbitrarily balancing selection size and FDR. Building on conformal e-variables and the e-Benjamini-Hochberg (e-BH) procedure, PH-CS is proved to provide a finite-sample post-hoc reliability guarantee whereby the ratio between estimated FDP level and true FDP is, on average, upper bounded by $1$, so that the average estimated FDP is, to first order, a valid upper bound on the true FDR. PH-CS is extended to control quality defined in terms of a general risk. Experiments on synthetic and real-world datasets demonstrate that, unlike CS, PH-CS can consistently satisfy user-imposed utility constraints while producing reliable FDP estimates and maintaining competitive FDR control.