On Large-Scale Multiple Testing Over Networks: An Asymptotic Approach

• URL: http://arxiv.org/abs/2211.16059v4
• Date: Sat, 16 Mar 2024 20:02:39 GMT
• Title: On Large-Scale Multiple Testing Over Networks: An Asymptotic Approach
• Authors: Mehrdad Pournaderi, Yu Xiang,
• Abstract summary: This work concerns developing communication- and computation-efficient methods for large-scale multiple testing over networks. We take an approach and propose two methods, proportion-matching and greedy aggregation, tailored to distributed settings. For both methods, we provide the rate of convergence for both the FDR and power.
• Score: 2.3072402651280517
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This work concerns developing communication- and computation-efficient methods for large-scale multiple testing over networks, which is of interest to many practical applications. We take an asymptotic approach and propose two methods, proportion-matching and greedy aggregation, tailored to distributed settings. The proportion-matching method achieves the global BH performance yet only requires a one-shot communication of the (estimated) proportion of true null hypotheses as well as the number of p-values at each node. By focusing on the asymptotic optimal power, we go beyond the BH procedure by providing an explicit characterization of the asymptotic optimal solution. This leads to the greedy aggregation method that effectively approximates the optimal rejection regions at each node, while computation efficiency comes from the greedy-type approach naturally. Moreover, for both methods, we provide the rate of convergence for both the FDR and power. Extensive numerical results over a variety of challenging settings are provided to support our theoretical findings.

Related papers

• Diffusion Stochastic Optimization for Min-Max Problems [33.73046548872663]
  The optimistic gradient method is useful in addressing minimax optimization problems. Motivated by the observation that the conventional version suffers from the need for a large batch size, we introduce and analyze a new formulation termed Samevareps-generativeOGOG.
  arXiv  Detail & Related papers  (2024-01-26T01:16:59Z)
• Optimizing Solution-Samplers for Combinatorial Problems: The Landscape of Policy-Gradient Methods [52.0617030129699]
  We introduce a novel theoretical framework for analyzing the effectiveness of DeepMatching Networks and Reinforcement Learning methods. Our main contribution holds for a broad class of problems including Max-and Min-Cut, Max-$k$-Bipartite-Bi, Maximum-Weight-Bipartite-Bi, and Traveling Salesman Problem. As a byproduct of our analysis we introduce a novel regularization process over vanilla descent and provide theoretical and experimental evidence that it helps address vanishing-gradient issues and escape bad stationary points.
  arXiv  Detail & Related papers  (2023-10-08T23:39:38Z)
• Sample Complexity for Quadratic Bandits: Hessian Dependent Bounds and Optimal Algorithms [64.10576998630981]
  We show the first tight characterization of the optimal Hessian-dependent sample complexity. A Hessian-independent algorithm universally achieves the optimal sample complexities for all Hessian instances. The optimal sample complexities achieved by our algorithm remain valid for heavy-tailed noise distributions.
  arXiv  Detail & Related papers  (2023-06-21T17:03:22Z)
• Boosting the Power of Kernel Two-Sample Tests [4.07125466598411]
  A kernel two-sample test based on the maximum mean discrepancy (MMD) is one of the most popular methods for detecting differences between two distributions over general metric spaces. We propose a method to boost the power of the kernel test by combining MMD estimates over multiple kernels using their Mahalanobis distance.
  arXiv  Detail & Related papers  (2023-02-21T14:14:30Z)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• Lower Bounds and Optimal Algorithms for Smooth and Strongly Convex Decentralized Optimization Over Time-Varying Networks [79.16773494166644]
  We consider the task of minimizing the sum of smooth and strongly convex functions stored in a decentralized manner across the nodes of a communication network. We design two optimal algorithms that attain these lower bounds. We corroborate the theoretical efficiency of these algorithms by performing an experimental comparison with existing state-of-the-art methods.
  arXiv  Detail & Related papers  (2021-06-08T15:54:44Z)
• Scalable Personalised Item Ranking through Parametric Density Estimation [53.44830012414444]
  Learning from implicit feedback is challenging because of the difficult nature of the one-class problem. Most conventional methods use a pairwise ranking approach and negative samplers to cope with the one-class problem. We propose a learning-to-rank approach, which achieves convergence speed comparable to the pointwise counterpart.
  arXiv  Detail & Related papers  (2021-05-11T03:38:16Z)
• Distributed Variational Bayesian Algorithms Over Sensor Networks [6.572330981878818]
  We propose two novel distributed VB algorithms for general Bayesian inference problem. The proposed algorithms have excellent performance, which are almost as good as the corresponding centralized VB algorithm relying on all data available in a fusion center.
  arXiv  Detail & Related papers  (2020-11-27T08:12:18Z)
• Adaptive Sampling for Best Policy Identification in Markov Decision Processes [79.4957965474334]
  We investigate the problem of best-policy identification in discounted Markov Decision (MDPs) when the learner has access to a generative model. The advantages of state-of-the-art algorithms are discussed and illustrated.
  arXiv  Detail & Related papers  (2020-09-28T15:22:24Z)
• Mean-Field Approximation to Gaussian-Softmax Integral with Application to Uncertainty Estimation [23.38076756988258]
  We propose a new single-model based approach to quantify uncertainty in deep neural networks. We use a mean-field approximation formula to compute an analytically intractable integral. Empirically, the proposed approach performs competitively when compared to state-of-the-art methods.
  arXiv  Detail & Related papers  (2020-06-13T07:32:38Z)
• A Hybrid-Order Distributed SGD Method for Non-Convex Optimization to Balance Communication Overhead, Computational Complexity, and Convergence Rate [28.167294398293297]
  We propose a method of distributed gradient descent (SGD) with low communication load and computational complexity, and still fast. To reduce the computational complexity in each iteration, the worker nodes approximate the directional derivatives with zeroth-order gradient estimation.
  arXiv  Detail & Related papers  (2020-03-27T14:02:15Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.