Pub Date : 2025-12-23DOI: 10.1109/TIT.2025.3643223
{"title":"IEEE Transactions on Information Theory Information for Authors","authors":"","doi":"10.1109/TIT.2025.3643223","DOIUrl":"https://doi.org/10.1109/TIT.2025.3643223","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 1","pages":"C3-C3"},"PeriodicalIF":2.9,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11313748","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145808628","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-23DOI: 10.1109/TIT.2025.3643249
{"title":"TechRxiv: Share Your Preprint Research with the World!","authors":"","doi":"10.1109/TIT.2025.3643249","DOIUrl":"https://doi.org/10.1109/TIT.2025.3643249","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 1","pages":"810-810"},"PeriodicalIF":2.9,"publicationDate":"2025-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11313722","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145808593","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-22DOI: 10.1109/TIT.2025.3646887
Housen Li;Zhi Liu;Axel Munk
Modern large-scale data analysis increasingly faces the challenge of achieving computational efficiency as well as statistical accuracy, as classical statistically efficient methods often fall short in the first regard. In the context of testing monotonicity of a regression function, we propose FOMT (Fast and Optimal Monotonicity Test), a novel methodology tailored to meet these dual demands. FOMT employs a sparse collection of local tests, strategically generated at random, to detect violations of monotonicity scattered throughout the domain of the regression function. This sparsity enables significant computational efficiency, achieving sublinear runtime in most cases, and quasilinear runtime (i.e. linear up to a log factor) in the worst case. In contrast, existing statistically optimal tests typically require at least quadratic runtime. FOMT’s statistical accuracy is achieved through the precise calibration of these local tests and their effective combination, ensuring both sensitivity to violations and control over false positives. More precisely, we show that FOMT separates the null and alternative hypotheses at minimax optimal rates over Hölder function classes of smoothness order in ($0,2$ ]. Further, when the smoothness is unknown, we introduce an adaptive version of FOMT, based on a modified Lepskii principle, which attains statistical optimality and meanwhile maintains the same computational complexity as if the intrinsic smoothness were known. Extensive simulations confirm the competitiveness and effectiveness of both FOMT and its adaptive variant.
{"title":"Adaptive Monotonicity Testing in Sublinear Time","authors":"Housen Li;Zhi Liu;Axel Munk","doi":"10.1109/TIT.2025.3646887","DOIUrl":"https://doi.org/10.1109/TIT.2025.3646887","url":null,"abstract":"Modern large-scale data analysis increasingly faces the challenge of achieving computational efficiency as well as statistical accuracy, as classical statistically efficient methods often fall short in the first regard. In the context of testing monotonicity of a regression function, we propose FOMT (Fast and Optimal Monotonicity Test), a novel methodology tailored to meet these dual demands. FOMT employs a sparse collection of <italic>local</i> tests, strategically generated at random, to detect violations of monotonicity scattered throughout the domain of the regression function. This sparsity enables significant computational efficiency, achieving sublinear runtime in most cases, and quasilinear runtime (i.e. linear up to a log factor) in the worst case. In contrast, existing statistically optimal tests typically require at least quadratic runtime. FOMT’s statistical accuracy is achieved through the precise calibration of these local tests and their effective combination, ensuring both sensitivity to violations and control over false positives. More precisely, we show that FOMT separates the null and alternative hypotheses at minimax optimal rates over Hölder function classes of smoothness order in (<inline-formula> <tex-math>$0,2$ </tex-math></inline-formula>]. Further, when the smoothness is unknown, we introduce an adaptive version of FOMT, based on a modified Lepskii principle, which attains statistical optimality and meanwhile maintains the same computational complexity as if the intrinsic smoothness were known. Extensive simulations confirm the competitiveness and effectiveness of both FOMT and its adaptive variant.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1240-1275"},"PeriodicalIF":2.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015914","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}
Pub Date : 2025-12-22DOI: 10.1109/TIT.2025.3647061
Huy Nguyen;Nhat Ho;Alessandro Rinaldo
Mixture of experts (MoE) has recently emerged as an effective framework for deploying machine learning models in a scalable and efficient way by softly dividing complex tasks among multiple specialized sub-models termed experts. Central to the success of MoE is an adaptive gating mechanism which determines the relevance of each expert to a given input and then dynamically assigns experts their respective weights. Despite its widespread use in practice, a comprehensive study on the effects of the softmax gating on the MoE has been lacking in the literature. To bridge this gap, we conduct a thorough theoretical analysis of the convergence rates for the problem of parameter estimation and expert estimation. We consider standard softmax gating and several variants, including a dense-to-sparse gating and a hierarchical softmax gating. Our theoretical results provide useful insights into the design of sample-efficient expert structures. In particular, we demonstrate that it requires polynomially many data points to estimate experts satisfying our proposed strong identifiability condition, namely a commonly used two-layer feed-forward network. In stark contrast, estimating linear experts, which violate the strong identifiability condition, necessitates exponentially many data points as a result of intrinsic parameter interactions, which we express in the language of partial differential equations.
{"title":"Convergence Rates for Softmax Gating Mixture of Experts","authors":"Huy Nguyen;Nhat Ho;Alessandro Rinaldo","doi":"10.1109/TIT.2025.3647061","DOIUrl":"https://doi.org/10.1109/TIT.2025.3647061","url":null,"abstract":"Mixture of experts (MoE) has recently emerged as an effective framework for deploying machine learning models in a scalable and efficient way by softly dividing complex tasks among multiple specialized sub-models termed experts. Central to the success of MoE is an adaptive gating mechanism which determines the relevance of each expert to a given input and then dynamically assigns experts their respective weights. Despite its widespread use in practice, a comprehensive study on the effects of the softmax gating on the MoE has been lacking in the literature. To bridge this gap, we conduct a thorough theoretical analysis of the convergence rates for the problem of parameter estimation and expert estimation. We consider standard softmax gating and several variants, including a dense-to-sparse gating and a hierarchical softmax gating. Our theoretical results provide useful insights into the design of sample-efficient expert structures. In particular, we demonstrate that it requires polynomially many data points to estimate experts satisfying our proposed <italic>strong identifiability</i> condition, namely a commonly used two-layer feed-forward network. In stark contrast, estimating linear experts, which violate the strong identifiability condition, necessitates exponentially many data points as a result of intrinsic parameter interactions, which we express in the language of partial differential equations.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1276-1304"},"PeriodicalIF":2.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015927","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}
Pub Date : 2025-12-22DOI: 10.1109/TIT.2025.3646804
Alon Kipnis
We study the problem of testing the goodness of fit of categorical count data to a Poisson distribution uniform over the categories, against a class of alternatives defined by excluding an $ell _{p}$ ball, $p leq 2$ , of radius $epsilon $ around the uniform rate sequence. We characterize the minimax risk for this problem as the expected number of samples $n$ and the number of categories $N$ go to infinity. Our result enables constant-factor comparisons among the many estimators previously proposed for this problem, rather than comparisons only at the level of convergence rates or scaling orders of sample complexity. The minimax test relies exclusively on collisions in the small sample limit, but behaves like the chi-squared test otherwise. Empirical studies across a range of parameters show that the asymptotic risk estimate is accurate in finite samples, and that the minimax test outperforms both the chi-squared test and a test based on collisions under the least favorable alternative. Our analysis involves a reduction to a structured subset of alternatives, establishing uniform asymptotic normality for a family of linear test statistics, and solving an optimization problem over $N$ -dimensional sequences akin to classical results from signal detection in Gaussian white noise. Finally, we discuss the connection to the fixed-sample-size multinomial model, arguing that the Poisson minimax risk derived here also characterizes the minimax risk of the multinomial problem.
{"title":"The Minimax Risk in Testing Uniformity Over Large Alphabets Under Missing-Ball Alternatives","authors":"Alon Kipnis","doi":"10.1109/TIT.2025.3646804","DOIUrl":"https://doi.org/10.1109/TIT.2025.3646804","url":null,"abstract":"We study the problem of testing the goodness of fit of categorical count data to a Poisson distribution uniform over the categories, against a class of alternatives defined by excluding an <inline-formula> <tex-math>$ell _{p}$ </tex-math></inline-formula> ball, <inline-formula> <tex-math>$p leq 2$ </tex-math></inline-formula>, of radius <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> around the uniform rate sequence. We characterize the minimax risk for this problem as the expected number of samples <inline-formula> <tex-math>$n$ </tex-math></inline-formula> and the number of categories <inline-formula> <tex-math>$N$ </tex-math></inline-formula> go to infinity. Our result enables constant-factor comparisons among the many estimators previously proposed for this problem, rather than comparisons only at the level of convergence rates or scaling orders of sample complexity. The minimax test relies exclusively on collisions in the small sample limit, but behaves like the chi-squared test otherwise. Empirical studies across a range of parameters show that the asymptotic risk estimate is accurate in finite samples, and that the minimax test outperforms both the chi-squared test and a test based on collisions under the least favorable alternative. Our analysis involves a reduction to a structured subset of alternatives, establishing uniform asymptotic normality for a family of linear test statistics, and solving an optimization problem over <inline-formula> <tex-math>$N$ </tex-math></inline-formula>-dimensional sequences akin to classical results from signal detection in Gaussian white noise. Finally, we discuss the connection to the fixed-sample-size multinomial model, arguing that the Poisson minimax risk derived here also characterizes the minimax risk of the multinomial problem.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"1831-1849"},"PeriodicalIF":2.9,"publicationDate":"2025-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11310811","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216606","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2025-12-19DOI: 10.1109/TIT.2025.3646470
Chung Shue Chen;Wing Shing Wong;Yuan-Hsun Lo;Tsai-Lien Wong
We investigate coding schemes that map source symbols into multisets of an alphabet. Such a formulation of source coding is an alternative approach to the traditional framework and is inspired by an object tracking problem over proximity sensor networks. We define a multiset combinatorial Gray code as a multiset code with fixed multiset cardinality that possesses combinatorial Gray code characteristic. For source codes that are organized as a grid, namely an integer lattice, we propose a solution by first constructing a mapping from the grid to the set of symbols, which we referred to as colors. The codes are then defined as the images of rectangular blocks in the grid of fixed dimensions. We refer to the mapping as a color mapping and the code as a color multiset code. We propose the idea of product multiset code that enables us to construct codes for high dimensional grids based on 1-dimensional (1D) grids. We provide a detailed analysis of color multiset codes on 1D grids, focusing on codes that require the minimal number of colors. To illustrate the application of such a coding scheme, we consider an object tracking problem on 2D grids and show its efficiency, which comes from exploiting transmission parallelism. Some numerical results are presented to conclude the paper.
{"title":"Multiset Combinatorial Gray Codes With Application to Proximity Sensor Networks","authors":"Chung Shue Chen;Wing Shing Wong;Yuan-Hsun Lo;Tsai-Lien Wong","doi":"10.1109/TIT.2025.3646470","DOIUrl":"https://doi.org/10.1109/TIT.2025.3646470","url":null,"abstract":"We investigate coding schemes that map source symbols into multisets of an alphabet. Such a formulation of source coding is an alternative approach to the traditional framework and is inspired by an object tracking problem over proximity sensor networks. We define a <italic>multiset combinatorial Gray code</i> as a multiset code with fixed multiset cardinality that possesses combinatorial Gray code characteristic. For source codes that are organized as a grid, namely an integer lattice, we propose a solution by first constructing a mapping from the grid to the set of symbols, which we referred to as colors. The codes are then defined as the images of rectangular blocks in the grid of fixed dimensions. We refer to the mapping as a <italic>color mapping</i> and the code as a <italic>color multiset code</i>. We propose the idea of product multiset code that enables us to construct codes for high dimensional grids based on 1-dimensional (1D) grids. We provide a detailed analysis of color multiset codes on 1D grids, focusing on codes that require the minimal number of colors. To illustrate the application of such a coding scheme, we consider an object tracking problem on 2D grids and show its efficiency, which comes from exploiting transmission parallelism. Some numerical results are presented to conclude the paper.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1378-1392"},"PeriodicalIF":2.9,"publicationDate":"2025-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015947","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}
Pub Date : 2025-12-16DOI: 10.1109/TIT.2025.3644744
Liyan Xie;Ruizhi Zhang
Sequential change detection is a fundamental problem in statistics and signal processing, with the CUSUM procedure widely used to achieve minimax detection delay under a prescribed false-alarm rate when pre- and post-change distributions are fully known. However, releasing CUSUM statistics and the corresponding stopping time directly can compromise individual data privacy. We therefore introduce a differentially private (DP) variant, called DP-CUSUM, that injects calibrated Laplace noise into both the vanilla CUSUM statistics and the detection threshold, preserving the recursive simplicity of the classical CUSUM statistics while ensuring per-sample differential privacy. We derive closed-form bounds on the average run length to false alarm and on the worst-case average detection delay, explicitly characterizing the trade-off among privacy level, false-alarm rate, and detection efficiency. Our theoretical results imply that under a weak privacy constraint, our proposed DP-CUSUM procedure achieves the same first-order asymptotic optimality as the classical, non-private CUSUM procedure. Numerical simulations are conducted to demonstrate the detection efficiency of our proposed DP-CUSUM under different privacy constraints, and the results are consistent with our theoretical findings.
{"title":"Sequential Change Detection With Differential Privacy","authors":"Liyan Xie;Ruizhi Zhang","doi":"10.1109/TIT.2025.3644744","DOIUrl":"https://doi.org/10.1109/TIT.2025.3644744","url":null,"abstract":"Sequential change detection is a fundamental problem in statistics and signal processing, with the CUSUM procedure widely used to achieve minimax detection delay under a prescribed false-alarm rate when pre- and post-change distributions are fully known. However, releasing CUSUM statistics and the corresponding stopping time directly can compromise individual data privacy. We therefore introduce a differentially private (DP) variant, called DP-CUSUM, that injects calibrated Laplace noise into both the vanilla CUSUM statistics and the detection threshold, preserving the recursive simplicity of the classical CUSUM statistics while ensuring per-sample differential privacy. We derive closed-form bounds on the average run length to false alarm and on the worst-case average detection delay, explicitly characterizing the trade-off among privacy level, false-alarm rate, and detection efficiency. Our theoretical results imply that under a weak privacy constraint, our proposed DP-CUSUM procedure achieves the same first-order asymptotic optimality as the classical, non-private CUSUM procedure. Numerical simulations are conducted to demonstrate the detection efficiency of our proposed DP-CUSUM under different privacy constraints, and the results are consistent with our theoretical findings.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1319-1331"},"PeriodicalIF":2.9,"publicationDate":"2025-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015937","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}
Pub Date : 2025-12-12DOI: 10.1109/TIT.2025.3643514
Mario Berta;Yongsheng Yao
The quantum dichotomies problem asks at what rate one pair of quantum states can be approximately mapped into another pair of quantum states. In the many copy limit and for vanishing error, the optimal rate is known to be given by the ratio of the respective quantum relative distances. Here, we study the large-deviation behavior of quantum dichotomies and determine the exact strong converse exponent based on the purified distance. This is the first time to establish the exact high-error large-deviation analysis for this task in fully quantum setting.
{"title":"Strong Converse Exponent of Quantum Dichotomies","authors":"Mario Berta;Yongsheng Yao","doi":"10.1109/TIT.2025.3643514","DOIUrl":"https://doi.org/10.1109/TIT.2025.3643514","url":null,"abstract":"The quantum dichotomies problem asks at what rate one pair of quantum states can be approximately mapped into another pair of quantum states. In the many copy limit and for vanishing error, the optimal rate is known to be given by the ratio of the respective quantum relative distances. Here, we study the large-deviation behavior of quantum dichotomies and determine the exact strong converse exponent based on the purified distance. This is the first time to establish the exact high-error large-deviation analysis for this task in fully quantum setting.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1212-1219"},"PeriodicalIF":2.9,"publicationDate":"2025-12-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015928","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}
Verifiable Secret-Sharing (VSS) is a fundamental primitive in secure distributed computing that allows a designated dealer to share a secret among n parties in the presence of an adversary controlling at most t of them. We study VSS in the presence of computationally-bounded adversaries. Known VSS protocols tolerate up to $t_{s} lt frac {n}{2}$ corruptions assuming a well-behaved synchronous network but become insecure when the network delay becomes unstable. On the other hand, solutions in the asynchronous model operate under arbitrary network conditions but only tolerate up to $t_{a} lt frac {n}{3}$ corruptions, even when the network is well-behaved. We aim to build a network-agnostic VSS protocol with the optimal threshold conditions. A network-agnostic protocol provides the best possible security guarantees, irrespective of the type of underlying communication network. Previously, network-agnostic VSS is known either with perfect security (Appan et al. IEEE IT 2023) where the threshold conditions are not known to be optimal or with statistical security (Appan et al. TCC 2023) where the threshold conditions are optimal, but the parties need to perform exponential amount of computation and communication. Using our VSS protocol, we design a secure Multi-Party Computation (MPC) protocol in the plain Public Key Infrastructure (PKI) model, i.e., without assuming an expensive trusted setup. Although our proposed MPC protocol incurs higher communication complexity than state-of-the-art network-agnostic MPC protocols, it motivates alternative directions for designing computationally inexpensive MPC protocols based on a plain PKI setup, which has not been explored in the domain of computationally secure network-agnostic MPC and offers valuable insights into designing it.
可验证秘密共享（VSS）是安全分布式计算中的一个基本元素，它允许指定的交易商在对手最多控制其中t方的情况下在n方之间共享秘密。我们在存在计算有界对手的情况下研究VSS。假设一个行为良好的同步网络，已知的VSS协议可以容忍高达$t_{s} lt frac {n}{2}$损坏，但当网络延迟变得不稳定时，它就变得不安全了。另一方面，异步模型中的解决方案在任意网络条件下运行，但只允许最多$t_{a} lt frac {n}{3}$损坏，即使网络运行良好。我们的目标是建立一个具有最优阈值条件的网络不可知VSS协议。无论底层通信网络的类型如何，网络无关协议都提供了最好的安全保证。以前，网络不可知的VSS要么具有完美的安全性（Appan等人）；IEEE IT 2023)，其中阈值条件不知道是最佳的或具有统计安全性（Appan等人）。TCC 2023)，其中阈值条件是最优的，但各方需要执行指数级的计算和通信。使用我们的VSS协议，我们在普通公钥基础设施（PKI）模型中设计了一个安全的多方计算（MPC）协议，即不假设昂贵的可信设置。尽管我们提出的MPC协议比最先进的网络无关MPC协议带来更高的通信复杂性，但它激发了基于普通PKI设置设计计算成本低廉的MPC协议的替代方向，这在计算安全的网络无关MPC领域尚未被探索，并为设计它提供了有价值的见解。
{"title":"Network-Agnostic Verifiable Secret Sharing With Cryptographic Security","authors":"Nidhish Bhimrajka;Ashish Choudhury;Supreeth Varadarajan","doi":"10.1109/TIT.2025.3642814","DOIUrl":"https://doi.org/10.1109/TIT.2025.3642814","url":null,"abstract":"<italic>Verifiable Secret-Sharing</i> (VSS) is a fundamental primitive in secure distributed computing that allows a designated dealer to share a secret among <italic>n</i> parties in the presence of an adversary controlling at most <italic>t</i> of them. We study VSS in the presence of <italic>computationally-bounded</i> adversaries. Known VSS protocols tolerate up to <inline-formula> <tex-math>$t_{s} lt frac {n}{2}$ </tex-math></inline-formula> corruptions assuming a well-behaved synchronous network but become insecure when the network delay becomes unstable. On the other hand, solutions in the asynchronous model operate under arbitrary network conditions but only tolerate up to <inline-formula> <tex-math>$t_{a} lt frac {n}{3}$ </tex-math></inline-formula> corruptions, even when the network is well-behaved. We aim to build a network-agnostic VSS protocol with the <italic>optimal</i> threshold conditions. A network-agnostic protocol provides the best possible security guarantees, irrespective of the type of underlying communication network. Previously, network-agnostic VSS is known either with <italic>perfect</i> security (Appan et al. IEEE IT 2023) where the threshold conditions are <italic>not</i> known to be optimal or with <italic>statistical security</i> (Appan et al. TCC 2023) where the threshold conditions are optimal, but the parties need to perform <italic>exponential</i> amount of computation and communication. Using our VSS protocol, we design a secure <italic>Multi-Party Computation</i> (MPC) protocol in the <italic>plain Public Key Infrastructure (PKI) model</i>, i.e., without assuming an expensive trusted setup. Although our proposed MPC protocol incurs higher communication complexity than state-of-the-art network-agnostic MPC protocols, it motivates alternative directions for designing <italic>computationally inexpensive</i> MPC protocols based on a plain PKI setup, which has not been explored in the domain of computationally secure network-agnostic MPC and offers valuable insights into designing it.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1332-1363"},"PeriodicalIF":2.9,"publicationDate":"2025-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015917","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}
Pub Date : 2025-12-08DOI: 10.1109/TIT.2025.3641166
Aytijhya Saha;Aaditya Ramdas
We propose an e-value based framework for testing arbitrary composite nulls against composite alternatives, when an $epsilon $ fraction of the data can be arbitrarily corrupted. Our tests are inherently sequential, being valid at arbitrary data-dependent stopping times, but they are new even for fixed sample sizes, giving type-I error control without any regularity conditions. We first prove that least favourable distribution (LFD) pairs, when they exist, yield optimal e-values for testing arbitrary composite nulls against composite alternatives. Then we show that if an LFD pair exists for some composite null and alternative, then the LFDs of Huber’s $epsilon $ -contamination or total variation (TV) neighborhoods around that specific pair form the optimal LFD pair for the corresponding robustified composite hypotheses. Furthermore, where LFDs do not exist, we develop new robust composite tests for general settings. Our test statistics are a nonnegative supermartingale under the (robust) null, even under a sequentially adaptive (non-i.i.d.) contamination model where the conditional distribution of each observation given the past data lies within an $epsilon $ TV ball of some distribution in the original composite null. When LFDs exist, our supermartingale grows to infinity exponentially fast under any distribution in the ($epsilon $ TV-corruption of the) alternative at the optimal rate. When LFDs do not exist, we provide an asymptotic growth rate analysis, showing that as $epsilon to 0$ , the exponent converges to the corresponding Kullback–Leibler divergence, recovering the classical optimal non-robust rate. Simulations validate the theory and demonstrate reasonable practical performance.
{"title":"Huber-Robust Likelihood Ratio Tests for Composite Nulls and Alternatives","authors":"Aytijhya Saha;Aaditya Ramdas","doi":"10.1109/TIT.2025.3641166","DOIUrl":"https://doi.org/10.1109/TIT.2025.3641166","url":null,"abstract":"We propose an e-value based framework for testing arbitrary composite nulls against composite alternatives, when an <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> fraction of the data can be arbitrarily corrupted. Our tests are inherently sequential, being valid at arbitrary data-dependent stopping times, but they are new even for fixed sample sizes, giving type-I error control without any regularity conditions. We first prove that least favourable distribution (LFD) pairs, when they exist, yield optimal e-values for testing arbitrary composite nulls against composite alternatives. Then we show that if an LFD pair exists for some composite null and alternative, then the LFDs of Huber’s <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula>-contamination or total variation (TV) neighborhoods around that specific pair form the optimal LFD pair for the corresponding robustified composite hypotheses. Furthermore, where LFDs do not exist, we develop new robust composite tests for general settings. Our test statistics are a nonnegative supermartingale under the (robust) null, even under a sequentially adaptive (non-i.i.d.) contamination model where the conditional distribution of each observation given the past data lies within an <inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> TV ball of some distribution in the original composite null. When LFDs exist, our supermartingale grows to infinity exponentially fast under any distribution in the (<inline-formula> <tex-math>$epsilon $ </tex-math></inline-formula> TV-corruption of the) alternative at the optimal rate. When LFDs do not exist, we provide an asymptotic growth rate analysis, showing that as <inline-formula> <tex-math>$epsilon to 0$ </tex-math></inline-formula>, the exponent converges to the corresponding Kullback–Leibler divergence, recovering the classical optimal non-robust rate. Simulations validate the theory and demonstrate reasonable practical performance.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 1","pages":"501-520"},"PeriodicalIF":2.9,"publicationDate":"2025-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145808601","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}
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