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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 First-Order Efficiency for Probabilistic Value Estimation via A Statistical Viewpoint Robust and Fast Training via Per-Sample Clipping
Signal Detection under Composite Hypotheses with Identica...
[Submitted on 29 Jul 2025 (v1), last revised 30 May 2026 (this v · 2026-06-02 · via stat updates on arXiv.org

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Abstract:In this paper, we consider the problem of detecting signals in multiple, sequentially observed data streams, where the distribution of each stream lies in one of two common composite spaces, depending on whether it is a signal or a noise. For this problem, we study a practical yet underexplored setting where it is a priori known that all signals have an identical distribution and so do all noises. Compared to the general setting where local distributions are free to take any values, this structure facilitates faster decision-making thanks to a smaller joint distribution space. However, it introduces additional challenges to the analysis of problem and design of tests, since the local distributions are now coupled. In this paper, we first establish a universal lower bound on the minimum expected sample size, which characterizes the essential difficulty of the problem and involves constants that are neither the minimum Kullback-Leibler divergences between the signal/noise distribution to the noise/signal distribution space, which appear in the lower bound for the general setting, nor the Kullback-Leibler divergences between the signal distribution and the noise distribution. Besides, we propose a test that controls the two types of familywise error rates below arbitrary levels, and achieves the minimum expected sample size asymptotically as the levels go to zero. Numerical studies are presented to compare with the state-of-the-art test for the general setting and demonstrate robustness against model misspecification.

Submission history

From: Yiming Xing [view email]
[v1] Tue, 29 Jul 2025 11:15:48 UTC (126 KB)
[v2] Sat, 30 May 2026 18:28:23 UTC (177 KB)