IEEE Transactions on Information Theory最新文献_第6页

Adversarial Phase Retrieval via Nonlinear Least Absolute Deviation 基于非线性最小绝对偏差的对抗相位检索

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-14 DOI: 10.1109/TIT.2025.3588879

Gao Huang;Song Li;Hang Xu

{"title":"Adversarial Phase Retrieval via Nonlinear Least Absolute Deviation","authors":"Gao Huang;Song Li;Hang Xu","doi":"10.1109/TIT.2025.3588879","DOIUrl":"https://doi.org/10.1109/TIT.2025.3588879","url":null,"abstract":"We investigate the phase retrieval problem perturbed by dense bounded noise and sparse outliers that can change an adversarially chosen <italic>s-fraction of the measurement vector. The adversarial sparse outliers may depend on both the observation and measurements. We demonstrate that the nonlinear least absolute deviation based on amplitude measurements can tolerate adversarial outliers up to a fraction of <inline-formula> <tex-math>$s^{*,1}approx 0.2043$ </tex-math></inline-formula>, while the intensity-based model can tolerate a fraction of <inline-formula> <tex-math>$s^{*,2}approx 0.1185$ </tex-math></inline-formula>. Furthermore, we construct adaptive counterexamples to show that these thresholds are theoretically sharp, thereby showing the presentation of phase transition in the adversarial phase retrieval problem when the corruption fraction exceeds the sharp thresholds. This implies that the amplitude-based model exhibits superior adversarial robustness in comparison with the intensity-based model. Corresponding experimental results are presented to further illustrate our theoretical findings. To the best of our knowledge, our results provide the first theoretical examination of the differences in robustness performance between amplitude and intensity measurement. A crucial aspect of our analysis is the exploration of the exact distribution of a combination of two non-independent Gaussian random variables, leading to the presentation of novel probability density functions to derive the sharp thresholds.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7396-7415"},"PeriodicalIF":2.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Tradeoffs Among Action Taking Policies Matter in Active Sequential Multi-Hypothesis Testing: The Optimal Error Exponent Region 主动序贯多假设检验中行动策略的权衡：最优误差指数区域

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-14 DOI: 10.1109/TIT.2025.3588527

Chia-Yu Hsu;I-Hsiang Wang

{"title":"Tradeoffs Among Action Taking Policies Matter in Active Sequential Multi-Hypothesis Testing: The Optimal Error Exponent Region","authors":"Chia-Yu Hsu;I-Hsiang Wang","doi":"10.1109/TIT.2025.3588527","DOIUrl":"https://doi.org/10.1109/TIT.2025.3588527","url":null,"abstract":"Reliability of sequential hypothesis testing can be greatly improved when the decision maker is given the freedom to adaptively take an action that determines the distribution of the current collected sample. Such advantage of sampling adaptivity has been realized since Chernoff’s seminal paper in 1959. While a large body of works have explored and investigated the gain of adaptivity, in the general multiple-hypothesis setting, the fundamental limits of individual error probabilities have not been fully understood. In particular, in the asymptotic regime as the expected stopping time tends to infinity, the error exponents are only characterized in specific cases, such as that of the total error probability. In this paper, we consider a general setup of active sequential multiple-hypothesis testing where at each time slot, a temporally varying subset of data sources (out of a known set) emerges from which the decision maker can select to collect samples, subject to a family of expected selection budget constraints. The selection of sources, understood as the “action” at each time slot, is constrained in a predefined action space. At the end of each time slot, the decision maker either decides to make the inference on the <italic>M hypotheses, or continues to observe the data sources for the next time slot. The optimal tradeoffs among <inline-formula> <tex-math>$M(M-1)$ </tex-math></inline-formula> types of error exponents are characterized. A companion asymptotically optimal test that strikes the balance between exploration and exploitation is proposed to achieve any target error exponents within the region. To the best of our knowledge, this is the first time in the literature to identify such tradeoffs among error exponents in active sequential hypothesis testing, and it uncovers the tension among different action taking policies even in the basic setting of Chernoff (1959).","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6546-6565"},"PeriodicalIF":2.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892396","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Griesmer and Optimal Linear Codes From the Affine Solomon–Stiffler Construction 仿射solomon - stiff结构的Griesmer和最优线性码

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-14 DOI: 10.1109/TIT.2025.3588778

Hao Chen

{"title":"Griesmer and Optimal Linear Codes From the Affine Solomon–Stiffler Construction","authors":"Hao Chen","doi":"10.1109/TIT.2025.3588778","DOIUrl":"https://doi.org/10.1109/TIT.2025.3588778","url":null,"abstract":"In their fundamental paper published in 1965, G. Solomon and J. J. Stiffler invented infinite families of codes meeting the Griesmer bound. These codes are then called Solomon-Stiffler codes and have motivated various constructions of codes meeting or close the Griesmer bound. However weight distributions of Solomon-Stiffler codes have been only determined for very special cases. In this paper, we give a geometric construction of affine and modified affine Solomon-Stiffler codes. Projective Solomon-Stiffler codes are special cases of our modified affine Solomon-Stiffler codes. Several infinite families of <italic>q-ary Griesmer, optimal, almost optimal, two-weight, three-weight, four-weight and five-weight linear codes are constructed as special cases of our construction. Weight distributions of these Griesmer, optimal or almost optimal codes are determined explicitly. Many optimal linear codes documented in Grassl’s list are re-constructed as (modified) affine Solomon-Stiffler codes. Several infinite families of optimal or Griesmer codes were constructed in Shi et, al., IEEE Trans. Inf. Theory, vol. 63, no. 10, 2017, and in Liu et, al., IEEE Trans. Inf. Theory, vol. 65, no. 5, 2019, via Gray images of codes over finite rings. Parameters and weight distributions of these Griesmer or optimal codes can be realized as very special cases in our construction. We also indicate that more general optimal binary linear codes than that constructed in Mondal, IEEE Trans. Inf. Theory, vol. 70, no. 7, 2024, can be obtained from subcodes of codimension one in the binary Solomon-Stiffler codes.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6834-6843"},"PeriodicalIF":2.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892351","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Signed Diverse Multiplex Networks: Clustering and Inference 签名多样多路网络：聚类与推理

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-14 DOI: 10.1109/TIT.2025.3588786

Marianna Pensky

{"title":"Signed Diverse Multiplex Networks: Clustering and Inference","authors":"Marianna Pensky","doi":"10.1109/TIT.2025.3588786","DOIUrl":"https://doi.org/10.1109/TIT.2025.3588786","url":null,"abstract":"The paper introduces a Signed Generalized Random Dot Product Graph (SGRDPG) model, which is a variant of the Generalized Random Dot Product Graph (GRDPG), where, in addition, edges can be positive or negative. The setting is extended to a multiplex version, where all layers have the same collection of nodes and follow the SGRDPG. The only common feature of the layers of the network is that they can be partitioned into groups with common subspace structures, while otherwise matrices of connection probabilities can be all different. The setting above is extremely flexible and includes a variety of existing multiplex network models, including GRDPG, as its particular cases. By employing novel methodologies, our paper ensures strongly consistent clustering of layers and highly accurate subspace estimation, which are significant improvements over the results of Pensky and Wang (2024). All algorithms and theoretical results in the paper remain true for both signed and binary networks. In addition, the paper shows that keeping signs of the edges in the process of network construction leads to a better precision of estimation and clustering and, hence, is beneficial for tackling real world problems such as, for example, analysis of brain networks.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7076-7096"},"PeriodicalIF":2.9,"publicationDate":"2025-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891260","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Model Free Prediction With Uncertainty Assessment 具有不确定性评估的无模型预测

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-11 DOI: 10.1109/TIT.2025.3588335

Yuling Jiao;Lican Kang;Jin Liu;Heng Peng;Heng Zuo

引用次数: 0

On the Second-Order Asymptotics of the Hoeffding Test and Other Divergence Tests 关于Hoeffding检验和其他散度检验的二阶渐近性

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-11 DOI: 10.1109/TIT.2025.3588194

K. V. Harsha;Jithin Ravi;Tobias Koch

{"title":"On the Second-Order Asymptotics of the Hoeffding Test and Other Divergence Tests","authors":"K. V. Harsha;Jithin Ravi;Tobias Koch","doi":"10.1109/TIT.2025.3588194","DOIUrl":"https://doi.org/10.1109/TIT.2025.3588194","url":null,"abstract":"Consider a composite hypothesis testing problem where the test has access to the null hypothesis <italic>P but not to the alternative hypothesis <italic>Q. The generalized likelihood-ratio test (GLRT) for this problem is the Hoeffding test, which accepts <italic>P if the Kullback-Leibler (KL) divergence between the empirical distribution of <inline-formula> <tex-math>$Z^{n}$ </tex-math></inline-formula> and <italic>P is below some threshold. This paper proposes a generalization of the Hoeffding test, termed divergence test, for which the KL divergence is replaced by an arbitrary divergence. For this test, the first and second-order terms of the type-II error probability for a fixed type-I error probability are characterized and compared with the error terms of the Neyman-Pearson test, which is the optimal test when both <italic>P and <italic>Q are known. It is demonstrated that, irrespective of the divergence, divergence tests achieve the first-order term of the Neyman-Pearson test. In contrast, the second-order term of divergence tests is strictly worse than that of the Neyman-Pearson test. It is further demonstrated that divergence tests with an invariant divergence achieve the same second-order term as the Hoeffding test, but divergence tests with a non-invariant divergence may outperform the Hoeffding test for some alternative hypotheses <italic>Q. This implies that the GLRT may have a second-order asymptotic performance that is strictly suboptimal.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 10","pages":"7459-7483"},"PeriodicalIF":2.9,"publicationDate":"2025-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145110258","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Lower Bounds for Error Coefficients of Griesmer Optimal Linear Codes via Iteration Griesmer最优线性码的迭代误差系数下界

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-10 DOI: 10.1109/TIT.2025.3587759

Chaofeng Guan;Shitao Li;Gaojun Luo;Zhi Ma;Hong Wang

{"title":"Lower Bounds for Error Coefficients of Griesmer Optimal Linear Codes via Iteration","authors":"Chaofeng Guan;Shitao Li;Gaojun Luo;Zhi Ma;Hong Wang","doi":"10.1109/TIT.2025.3587759","DOIUrl":"https://doi.org/10.1109/TIT.2025.3587759","url":null,"abstract":"The error coefficient of a linear code is defined as the number of minimum-weight codewords. In an additive white Gaussian noise channel, optimal linear codes with the smallest error coefficients achieve the best possible asymptotic frame error rate (AFER) among all optimal linear codes under maximum likelihood decoding. Such codes are referred to as AFER-optimal linear codes. The Griesmer bound is essential for determining the optimality of linear codes. However, establishing tight lower bounds on the error coefficients of Griesmer optimal linear codes is challenging, and the linear programming bound often performs inadequately. In this paper, we propose several iterative lower bounds for the error coefficients of Griesmer optimal linear codes. Specifically, for binary linear codes, our bounds are tight in most cases when the dimension does not exceed 5. To evaluate the performance of our bounds when they are not tight, we also determine the parameters of the remaining 5-dimensional AFER-optimal linear codes. Our final comparison demonstrates that even when our bounds are not tight, they remain very close to the actual values, with a gap of less than or equal to 2.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"6820-6833"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144892397","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Robust Offline Reinforcement Learning for Non-Markovian Decision Processes 非马尔可夫决策过程的鲁棒离线强化学习

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-10 DOI: 10.1109/TIT.2025.3587509

Ruiquan Huang;Yingbin Liang;Jing Yang

{"title":"Robust Offline Reinforcement Learning for Non-Markovian Decision Processes","authors":"Ruiquan Huang;Yingbin Liang;Jing Yang","doi":"10.1109/TIT.2025.3587509","DOIUrl":"https://doi.org/10.1109/TIT.2025.3587509","url":null,"abstract":"Distributionally robust offline reinforcement learning (RL) aims to find a policy that performs the best under the worst environment within an uncertainty set using an offline dataset collected from a nominal model. While recent advances in robust RL focus on Markov decision processes (MDPs), robust non-Markovian RL is limited to planning problem where the transitions in the uncertainty set are known. In this paper, we study the learning problem of robust offline non-Markovian RL. Specifically, when the nominal model admits a low-rank structure, we propose a new algorithm, featuring a novel dataset distillation and a lower confidence bound (LCB) design for robust values under different types of the uncertainty set. We also derive new dual forms for these robust values in non-Markovian RL, making our algorithm more amenable to practical implementation. By further introducing a novel type-I concentrability coefficient tailored for offline low-rank non-Markovian decision processes, we prove that our algorithm can find an <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>-optimal robust policy using <inline-formula> <tex-math>$O(1/epsilon ^{2})$ </tex-math></inline-formula> offline samples. Moreover, we extend our algorithm to the case when the nominal model does not have specific structure. With a new type-II concentrability coefficient, the extended algorithm also enjoys polynomial sample efficiency under all different types of the uncertainty set.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"71 9","pages":"7208-7228"},"PeriodicalIF":2.9,"publicationDate":"2025-07-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144891181","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Computationally Efficient Reductions Between Some Statistical Models 一些统计模型之间的计算效率约简

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-10 DOI: 10.1109/TIT.2025.3587354

Mengqi Lou;Guy Bresler;Ashwin Pananjady

引用次数: 0

Continuity Bounds for Quantum Entropies Arising From a Fundamental Entropic Inequality 由基本熵不等式引起的量子熵的连续界

IF 2.9 3区计算机科学

IEEE Transactions on Information Theory Pub Date : 2025-07-08 DOI: 10.1109/TIT.2025.3586478

Koenraad Audenaert;Bjarne Bergh;Nilanjana Datta;Michael G. Jabbour;Ángela Capel;Paul Gondolf

引用次数: 0