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8,552 results on '"Gao, Rui"'

195. Robust Hypothesis Testing with Wasserstein Uncertainty Sets

Author

Xie, Liyan, Gao, Rui, and Xie, Yao

Subjects
Mathematics - Statistics Theory, Statistics - Methodology
Abstract

We consider a data-driven robust hypothesis test where the optimal test will minimize the worst-case performance regarding distributions that are close to the empirical distributions with respect to the Wasserstein distance. This leads to a new non-parametric hypothesis testing framework based on distributionally robust optimization, which is more robust when there are limited samples for one or both hypotheses. Such a scenario often arises from applications such as health care, online change-point detection, and anomaly detection. We study the computational and statistical properties of the proposed test by presenting a tractable convex reformulation of the original infinite-dimensional variational problem exploiting Wasserstein's properties and characterizing the radii selection for the uncertainty sets. We also demonstrate the good performance of our method on synthetic and real data.

Published
2021

196. Regularity of calibrated sub-actions for circle expanding maps and Sturmian optimization

Author

Gao, Rui

Subjects
Mathematics - Dynamical Systems
Abstract

In this short and elementary note, we study some ergodic optimization problems for circle expanding maps. We first make an observation that if a function is not far from being convex, then its calibrated sub-actions are closer to convex functions in certain effective way. As an application of this simple observation, for circle doubling map, we generalize a result of Bousch saying that translations of the cosine function are uniquely optimized by Sturmian measures. Our argument follows the mainline of Bousch's original proof, while the technical part is simplified by the observation mentioned above, and no numerical calculation is needed., Comment: 11 pages

Published
2021

197. Hierarchical Non-Stationary Temporal Gaussian Processes With $L^1$-Regularization

Author

Zhao, Zheng, Gao, Rui, and Särkkä, Simo

Subjects
Statistics - Methodology, Statistics - Computation, Statistics - Machine Learning
Abstract

This paper is concerned with regularized extensions of hierarchical non-stationary temporal Gaussian processes (NSGPs) in which the parameters (e.g., length-scale) are modeled as GPs. In particular, we consider two commonly used NSGP constructions which are based on explicitly constructed non-stationary covariance functions and stochastic differential equations, respectively. We extend these NSGPs by including $L^1$-regularization on the processes in order to induce sparseness. To solve the resulting regularized NSGP (R-NSGP) regression problem we develop a method based on the alternating direction method of multipliers (ADMM) and we also analyze its convergence properties theoretically. We also evaluate the performance of the proposed methods in simulated and real-world datasets., Comment: 20 pages. Submitted to Statistics and Computing

Published
2021

198. Secure and practical multiparty quantum digital signatures

Author

Weng, Chen-Xun, Lu, Yu-Shuo, Gao, Rui-Qi, Xie, Yuan-Mei, Gu, Jie, Li, Chen-Long, Li, Bing-Hong, Yin, Hua-Lei, and Chen, Zeng-Bing

Subjects
Quantum Physics
Abstract

Quantum digital signatures (QDSs) promise information-theoretic security against repudiation and forgery of messages. Compared with currently existing three-party QDS protocols, multiparty protocols have unique advantages in the practical case of more than two receivers when sending a mass message. However, complex security analysis, numerous quantum channels and low data utilization efficiency make it intractable to expand three-party to multiparty scenario. Here, based on six-state non-orthogonal encoding protocol, we propose an effective multiparty QDS framework to overcome these difficulties. The number of quantum channels in our protocol only linearly depends on the number of users. The post-matching method is introduced to enhance data utilization efficiency and make it linearly scale with the probability of detection events even for five-party scenario. Our work compensates for the absence of practical multiparty protocols, which paves the way for future QDS networks., Comment: 9 pages, 6 figures

Published
2021
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