arXiv - MATH - Statistics Theory最新文献_第3页

High-arity PAC learning via exchangeability 通过可交换性促进 PAC 学习

arXiv - MATH - Statistics Theory Pub Date : 2024-02-22 DOI: arxiv-2402.14294

Leonardo N. Coregliano, Maryanthe Malliaris

引用次数: 0

Learning Properties of Quantum States Without the I.I.D. Assumption 没有 I.I.D. 假设的量子态学习特性

arXiv - MATH - Statistics Theory Pub Date : 2024-01-30 DOI: arxiv-2401.16922

Omar Fawzi, Richard Kueng, Damian Markham, Aadil Oufkir

{"title":"Learning Properties of Quantum States Without the I.I.D. Assumption","authors":"Omar Fawzi, Richard Kueng, Damian Markham, Aadil Oufkir","doi":"arxiv-2401.16922","DOIUrl":"https://doi.org/arxiv-2401.16922","url":null,"abstract":"We develop a framework for learning properties of quantum states beyond the\u0000assumption of independent and identically distributed (i.i.d.) input states. We\u0000prove that, given any learning problem (under reasonable assumptions), an\u0000algorithm designed for i.i.d. input states can be adapted to handle input\u0000states of any nature, albeit at the expense of a polynomial increase in copy\u0000complexity. Furthermore, we establish that algorithms which perform\u0000non-adaptive incoherent measurements can be extended to encompass non-i.i.d.\u0000input states while maintaining comparable error probabilities. This allows us,\u0000among others applications, to generalize the classical shadows of Huang, Kueng,\u0000and Preskill to the non-i.i.d. setting at the cost of a small loss in\u0000efficiency. Additionally, we can efficiently verify any pure state using\u0000Clifford measurements, in a way that is independent of the ideal state. Our\u0000main techniques are based on de Finetti-style theorems supported by tools from\u0000information theory. In particular, we prove a new randomized local de Finetti\u0000theorem that can be of independent interest.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"12 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646771","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Finite-Time Frequentist Regret Bounds of Multi-Agent Thompson Sampling on Sparse Hypergraphs 稀疏超图上多代理汤普森采样的有限时间频数后悔约束

arXiv - MATH - Statistics Theory Pub Date : 2023-12-24 DOI: arxiv-2312.15549

Tianyuan Jin, Hao-Lun Hsu, William Chang, Pan Xu

{"title":"Finite-Time Frequentist Regret Bounds of Multi-Agent Thompson Sampling on Sparse Hypergraphs","authors":"Tianyuan Jin, Hao-Lun Hsu, William Chang, Pan Xu","doi":"arxiv-2312.15549","DOIUrl":"https://doi.org/arxiv-2312.15549","url":null,"abstract":"We study the multi-agent multi-armed bandit (MAMAB) problem, where $m$ agents\u0000are factored into $rho$ overlapping groups. Each group represents a hyperedge,\u0000forming a hypergraph over the agents. At each round of interaction, the learner\u0000pulls a joint arm (composed of individual arms for each agent) and receives a\u0000reward according to the hypergraph structure. Specifically, we assume there is\u0000a local reward for each hyperedge, and the reward of the joint arm is the sum\u0000of these local rewards. Previous work introduced the multi-agent Thompson\u0000sampling (MATS) algorithm citep{verstraeten2020multiagent} and derived a\u0000Bayesian regret bound. However, it remains an open problem how to derive a\u0000frequentist regret bound for Thompson sampling in this multi-agent setting. To\u0000address these issues, we propose an efficient variant of MATS, the\u0000$epsilon$-exploring Multi-Agent Thompson Sampling ($epsilon$-MATS) algorithm,\u0000which performs MATS exploration with probability $epsilon$ while adopts a\u0000greedy policy otherwise. We prove that $epsilon$-MATS achieves a worst-case\u0000frequentist regret bound that is sublinear in both the time horizon and the\u0000local arm size. We also derive a lower bound for this setting, which implies\u0000our frequentist regret upper bound is optimal up to constant and logarithm\u0000terms, when the hypergraph is sufficiently sparse. Thorough experiments on\u0000standard MAMAB problems demonstrate the superior performance and the improved\u0000computational efficiency of $epsilon$-MATS compared with existing algorithms\u0000in the same setting.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139057142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Debiasing Welch's Method for Spectral Density Estimation 用于频谱密度估计的去偏差韦尔奇方法

arXiv - MATH - Statistics Theory Pub Date : 2023-12-21 DOI: arxiv-2312.13643

Lachlan C. Astfalck, Adam M. Sykulski, Edward J. Cripps

{"title":"Debiasing Welch's Method for Spectral Density Estimation","authors":"Lachlan C. Astfalck, Adam M. Sykulski, Edward J. Cripps","doi":"arxiv-2312.13643","DOIUrl":"https://doi.org/arxiv-2312.13643","url":null,"abstract":"Welch's method provides an estimator of the power spectral density that is\u0000statistically consistent. This is achieved by averaging over periodograms\u0000calculated from overlapping segments of a time series. For a finite length time\u0000series, while the variance of the estimator decreases as the number of segments\u0000increase, the magnitude of the estimator's bias increases: a bias-variance\u0000trade-off ensues when setting the segment number. We address this issue by\u0000providing a a novel method for debiasing Welch's method which maintains the\u0000computational complexity and asymptotic consistency, and leads to improved\u0000finite-sample performance. Theoretical results are given for fourth-order\u0000stationary processes with finite fourth-order moments and absolutely continuous\u0000fourth-order cumulant spectrum. The significant bias reduction is demonstrated\u0000with numerical simulation and an application to real-world data, where several\u0000empirical metrics indicate our debiased estimator compares favourably to\u0000Welch's. Our estimator also permits irregular spacing over frequency and we\u0000demonstrate how this may be employed for signal compression and further\u0000variance reduction. Code accompanying this work is available in the R and\u0000python languages.","PeriodicalId":501330,"journal":{"name":"arXiv - MATH - Statistics Theory","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139028939","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Matching prior pairs connecting Maximum A Posteriori estimation and posterior expectation 连接最大后验估计和后验期望的匹配先验对

arXiv - MATH - Statistics Theory Pub Date : 2023-12-15 DOI: arxiv-2312.09586

Michiko Okudo, Keisuke Yano

引用次数: 0

Set-valued expectiles for ordered data analysis 用于有序数据分析的集值期望值

arXiv - MATH - Statistics Theory Pub Date : 2023-12-15 DOI: arxiv-2312.09930

Ha Thi Khanh Linh, Andreas H Hamel

引用次数: 0

Matroid Stratification of ML Degrees of Independence Models ML 独立度模型的矩阵分层

arXiv - MATH - Statistics Theory Pub Date : 2023-12-15 DOI: arxiv-2312.10010

Oliver Clarke, Serkan Hoşten, Nataliia Kushnerchuk, Janike Oldekop