Finite-Sample FDR Control for Greedy Aggregation over Networks
Abstract
Distributed multiple testing asks N sites, each holding p-values for its own hypotheses, to control the false discovery rate (FDR) of the discoveries made across the whole network while communicating only a small number of bits. Greedy interval aggregation (Pournaderi and Xiang, IEEE TSIPN, 2023) meets the communication budget but controls FDR only asymptotically, and its FDR can exceed the target at finite sample sizes; the same interval counts both select the rejection regions and calibrate the stopping rule, which biases the selected interval densities upward. We propose \emph{budgeted BONuS-GA}: each site mixes synthetic uniform p-values into its data, the center ranks candidate p-value intervals across sites using the pooled counts, and each site's false discoveries are estimated from its own synthetic counts under a per-site share of the level. The procedure needs no knowledge of the null proportions, uses every p-value for both selection and inference, and controls FDR≤α at every sample size for any fixed assignment of hypotheses to sites, assuming only that the null p-values are independent uniforms, independent of the non-null p-values. It keeps the original O(√mlog m) communication, m being the total number of p-values, when N=O(√m). We also give a sample-splitting alternative, cross-fit greedy aggregation, with finite-sample control under a random-site model, and we quantify the selection bias behind the original procedure's failure. In a monitoring-network simulation the budgeted procedure retains most of the power of its heuristic counterpart at moderate-to-large site sizes.
Related
- Lifting Finite-Sample Gaussian Approximation of Wide Neural Networks to Functional Convergence
- Minimum-Energy Control for Stochastic Linear Systems: A Data-Driven Approach with Finite-Sample Guarantees
- Diffusion Score Estimation with Shallow Neural Networks: Regularity, Approximation, and Finite-Sample Rates
- Finite-Time Synchronization of Discontinuous Fractional-Order Multi-Layer Coupled Neural Networks via Aperiodic Intermittent Control
- Greedy Orthogonal Polynomial Manifolds with Lipschitz Control for Dimensionality Reduction and Reduced Modeling
BibTeX
@misc{pournaderi2026finitesample,
title = {{Finite-Sample FDR Control for Greedy Aggregation over Networks}},
author = {Mehrdad Pournaderi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.14170},
eprint = {2609.14170},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.14170},
}
RIS
TY - UNPB
TI - Finite-Sample FDR Control for Greedy Aggregation over Networks
AU - Mehrdad Pournaderi
PY - 2026
DA - 2026/10/07
PB - arXiv
DO - 10.48550/arxiv.2609.14170
UR - https://arxiv.org/abs/2609.14170
AB - Distributed multiple testing asks N sites, each holding p-values for its own hypotheses, to control the false discovery rate (FDR) of the discoveries made across the whole network while communicating only a small number of bits. Greedy interval aggregation (Pournaderi and Xiang, IEEE TSIPN, 2023) meets the communication budget but controls FDR only asymptotically, and its FDR can exceed the target at finite sample sizes; the same interval counts both select the rejection regions and calibrate the stopping rule, which biases the selected interval densities upward. We propose \emph{budgeted BONuS-GA}: each site mixes synthetic uniform p-values into its data, the center ranks candidate p-value intervals across sites using the pooled counts, and each site's false discoveries are estimated from its own synthetic counts under a per-site share of the level. The procedure needs no knowledge of the null proportions, uses every p-value for both selection and inference, and controls FDR≤α at every sample size for any fixed assignment of hypotheses to sites, assuming only that the null p-values are independent uniforms, independent of the non-null p-values. It keeps the original O(√mlog m) communication, m being the total number of p-values, when N=O(√m). We also give a sample-splitting alternative, cross-fit greedy aggregation, with finite-sample control under a random-site model, and we quantify the selection bias behind the original procedure's failure. In a monitoring-network simulation the budgeted procedure retains most of the power of its heuristic counterpart at moderate-to-large site sizes.
ER -