Pub Date : 2026-02-19DOI: 10.1109/TIT.2026.3662262
{"title":"IEEE Transactions on Information Theory Information for Authors","authors":"","doi":"10.1109/TIT.2026.3662262","DOIUrl":"https://doi.org/10.1109/TIT.2026.3662262","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"C3-C3"},"PeriodicalIF":2.9,"publicationDate":"2026-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11400650","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216615","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 : 2026-02-19DOI: 10.1109/TIT.2026.3663823
{"title":"TechRxiv: Share Your Preprint Research with the World!","authors":"","doi":"10.1109/TIT.2026.3663823","DOIUrl":"https://doi.org/10.1109/TIT.2026.3663823","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"2028-2028"},"PeriodicalIF":2.9,"publicationDate":"2026-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11400675","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216531","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 : 2026-01-23DOI: 10.1109/TIT.2026.3657603
Namhun Koo;Soonhak Kwon
In this paper, we investigate the differential and boomerang properties of a class of binomial $F_{r,u}(x) = x^{r}(1 + uchi (x))$ over the finite field $mathbb {F}_{p^{n}}$ , where $r = frac {p^{n}+1}{4}$ , $p^{n} equiv 3 pmod {4}$ , and $chi (x) = x^{frac {p^{n} -1}{2}}$ is the quadratic character in $mathbb {F}_{p^{n}}$ . We show that $F_{r,pm 1}$ is locally-PN with boomerang uniformity 0 when $p^{n} equiv 3 pmod {8}$ . To the best of our knowledge, it is the second known non-PN function class with boomerang uniformity 0, and the first such example over odd characteristic fields with $p gt 3$ . Moreover, we show that $F_{r,pm 1}$ is locally-APN with boomerang uniformity at most 2 when $p^{n} equiv 7 pmod {8}$ . We also provide complete classifications of the differential and boomerang spectra of $F_{r,pm 1}$ . Furthermore, we thoroughly investigate the differential uniformity of $F_{r,u}$ for $uin mathbb {F}_{p^{n}}^{*} setminus {pm 1}$ .
{"title":"On Differential and Boomerang Properties of a Class of Binomials Over Finite Fields of Odd Characteristic","authors":"Namhun Koo;Soonhak Kwon","doi":"10.1109/TIT.2026.3657603","DOIUrl":"https://doi.org/10.1109/TIT.2026.3657603","url":null,"abstract":"In this paper, we investigate the differential and boomerang properties of a class of binomial <inline-formula> <tex-math>$F_{r,u}(x) = x^{r}(1 + uchi (x))$ </tex-math></inline-formula> over the finite field <inline-formula> <tex-math>$mathbb {F}_{p^{n}}$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$r = frac {p^{n}+1}{4}$ </tex-math></inline-formula>, <inline-formula> <tex-math>$p^{n} equiv 3 pmod {4}$ </tex-math></inline-formula>, and <inline-formula> <tex-math>$chi (x) = x^{frac {p^{n} -1}{2}}$ </tex-math></inline-formula> is the quadratic character in <inline-formula> <tex-math>$mathbb {F}_{p^{n}}$ </tex-math></inline-formula>. We show that <inline-formula> <tex-math>$F_{r,pm 1}$ </tex-math></inline-formula> is locally-PN with boomerang uniformity 0 when <inline-formula> <tex-math>$p^{n} equiv 3 pmod {8}$ </tex-math></inline-formula>. To the best of our knowledge, it is the second known non-PN function class with boomerang uniformity 0, and the first such example over odd characteristic fields with <inline-formula> <tex-math>$p gt 3$ </tex-math></inline-formula>. Moreover, we show that <inline-formula> <tex-math>$F_{r,pm 1}$ </tex-math></inline-formula> is locally-APN with boomerang uniformity at most 2 when <inline-formula> <tex-math>$p^{n} equiv 7 pmod {8}$ </tex-math></inline-formula>. We also provide complete classifications of the differential and boomerang spectra of <inline-formula> <tex-math>$F_{r,pm 1}$ </tex-math></inline-formula>. Furthermore, we thoroughly investigate the differential uniformity of <inline-formula> <tex-math>$F_{r,u}$ </tex-math></inline-formula> for <inline-formula> <tex-math>$uin mathbb {F}_{p^{n}}^{*} setminus {pm 1}$ </tex-math></inline-formula>.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"1928-1942"},"PeriodicalIF":2.9,"publicationDate":"2026-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216662","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 : 2026-01-22DOI: 10.1109/TIT.2026.3651883
{"title":"IEEE Transactions on Information Theory Information for Authors","authors":"","doi":"10.1109/TIT.2026.3651883","DOIUrl":"https://doi.org/10.1109/TIT.2026.3651883","url":null,"abstract":"","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"C3-C3"},"PeriodicalIF":2.9,"publicationDate":"2026-01-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/stamp/stamp.jsp?tp=&arnumber=11361354","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015946","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 : 2026-01-14DOI: 10.1109/TIT.2026.3654430
Amirreza Zamani;Mikael Skoglund
We study two semantic communication problems with privacy constraints considering single-task and multi-task scenarios. In both scenarios, an encoder has access to an information source arbitrarily correlated with some latent private information. In the single-task scenario, a user has a task, and the encoder designs a message to be revealed, which is called the semantic of the information source. Due to the privacy constraints, the semantic cannot be disclosed directly, so the encoder adds noise to produce data that can be disclosed. The goal is to design the disclosed message that maximizes the utility attained by the user while satisfying a privacy constraint. In the multi-task scenario, the user has $L$ tasks with priorities. Similarly, the encoder designs the disclosed message by adding noise to the semantic, which is optimized for the intended tasks. The goal is to design a mechanism to produce the disclosed message that maximizes the weighted sum of the utilities achieved by the user while satisfying a privacy constraint on the private data. In this work, we first consider the single-task scenario and design the added noise utilizing various methods, including the extended versions of the Functional Representation Lemma, Strong Functional Representation Lemma, and the separation technique. By designing the added noise, we obtain lower bounds with constructive proofs. We then study the multi-task scenario and derive a simple privacy mechanism design considering the source semantics. We show that in the multi-task scenario the main problem can be divided into multiple parallel single-task problems. In both scenarios, the obtained lower and upper bounds are studied considering different cases to study their tightness. We show that under some assumptions our proposed designs are optimal. We provide a few numerical experiments based on the MNIST dataset and medical applications to illustrate the designs and evaluate the bounds, considering both single and multi-task scenarios. Finally, we study an application where a semantic communication with two separate blind encoders is considered.
{"title":"Multi-Task Semantic Communications With Bounded Privacy Leakage Constraint","authors":"Amirreza Zamani;Mikael Skoglund","doi":"10.1109/TIT.2026.3654430","DOIUrl":"https://doi.org/10.1109/TIT.2026.3654430","url":null,"abstract":"We study two semantic communication problems with privacy constraints considering single-task and multi-task scenarios. In both scenarios, an encoder has access to an information source arbitrarily correlated with some latent private information. In the single-task scenario, a user has a task, and the encoder designs a message to be revealed, which is called the semantic of the information source. Due to the privacy constraints, the semantic cannot be disclosed directly, so the encoder adds noise to produce data that can be disclosed. The goal is to design the disclosed message that maximizes the utility attained by the user while satisfying a privacy constraint. In the multi-task scenario, the user has <inline-formula> <tex-math>$L$ </tex-math></inline-formula> tasks with priorities. Similarly, the encoder designs the disclosed message by adding noise to the semantic, which is optimized for the intended tasks. The goal is to design a mechanism to produce the disclosed message that maximizes the weighted sum of the utilities achieved by the user while satisfying a privacy constraint on the private data. In this work, we first consider the single-task scenario and design the added noise utilizing various methods, including the extended versions of the Functional Representation Lemma, Strong Functional Representation Lemma, and the separation technique. By designing the added noise, we obtain lower bounds with constructive proofs. We then study the multi-task scenario and derive a simple privacy mechanism design considering the source semantics. We show that in the multi-task scenario the main problem can be divided into multiple parallel single-task problems. In both scenarios, the obtained lower and upper bounds are studied considering different cases to study their tightness. We show that under some assumptions our proposed designs are optimal. We provide a few numerical experiments based on the MNIST dataset and medical applications to illustrate the designs and evaluate the bounds, considering both single and multi-task scenarios. Finally, we study an application where a semantic communication with two separate blind encoders is considered.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"1900-1927"},"PeriodicalIF":2.9,"publicationDate":"2026-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216534","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 : 2026-01-12DOI: 10.1109/TIT.2026.3651210
Saar Tarnopolsky;Alejandro Cohen
We introduce a novel hybrid universal network coding cryptosystem (NU-HUNCC) for non-uniform messages in the finite blocklength regime that provides Post-Quantum (PQ) security at high communication rates. Recently, hybrid cryptosystems offered PQ security by premixing the data using secure linear coding schemes and encrypting only a small portion of it. The data is assumed to be uniformly distributed, an assumption that is often challenging to enforce. Standard fixed-length lossless source coding and compression schemes guarantee a uniform output in normalized divergence. Yet, this is not sufficient to guarantee security. We consider an efficient compression scheme uniform in non-normalized variational distance, that by utilizing a uniform sub-linear shared seed, guarantees PQ security. Specifically, for the proposed PQ cryptosystem, first, we provide an end-to-end practical coding scheme, NU-HUNCC, for non-uniform messages. Second, we show that NU-HUNCC is information-theoretic individually secured (IS) against an eavesdropper with access to any subset of the links and provide a converse proof against such an eavesdropper. Third, we introduce a modified security definition, individual semantic security under a chosen ciphertext attack (ISS-CCA1), and show that against an all-observing eavesdropper, NU-HUNCC satisfies its conditions. Finally, we provide an analysis of NU-HUNCC’s high data rate, low computational complexity, and the negligibility of the shared seed size.
{"title":"Coding-Based Hybrid Post-Quantum Cryptosystem for Non-Uniform Information","authors":"Saar Tarnopolsky;Alejandro Cohen","doi":"10.1109/TIT.2026.3651210","DOIUrl":"https://doi.org/10.1109/TIT.2026.3651210","url":null,"abstract":"We introduce a novel hybrid universal network coding cryptosystem (NU-HUNCC) for non-uniform messages in the finite blocklength regime that provides Post-Quantum (PQ) security at high communication rates. Recently, hybrid cryptosystems offered PQ security by premixing the data using secure linear coding schemes and encrypting only a small portion of it. The data is assumed to be uniformly distributed, an assumption that is often challenging to enforce. Standard fixed-length lossless source coding and compression schemes guarantee a uniform output in <italic>normalized divergence</i>. Yet, this is not sufficient to guarantee security. We consider an efficient compression scheme uniform in <italic>non-normalized variational distance</i>, that by utilizing a uniform sub-linear shared seed, guarantees PQ security. Specifically, for the proposed PQ cryptosystem, first, we provide an end-to-end practical coding scheme, NU-HUNCC, for non-uniform messages. Second, we show that NU-HUNCC is information-theoretic individually secured (IS) against an eavesdropper with access to any subset of the links and provide a converse proof against such an eavesdropper. Third, we introduce a modified security definition, individual semantic security under a chosen ciphertext attack (ISS-CCA1), and show that against an all-observing eavesdropper, NU-HUNCC satisfies its conditions. Finally, we provide an analysis of NU-HUNCC’s high data rate, low computational complexity, and the negligibility of the shared seed size.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"1850-1873"},"PeriodicalIF":2.9,"publicationDate":"2026-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216526","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 : 2026-01-05DOI: 10.1109/TIT.2026.3650970
Gi-Ren Liu;Yuan-Chung Sheu;Hau-Tieng Wu
Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the time-frequency domain when the input is a random process remains underexplored. In this work, we study the magnitude and phase of the AWT as random fields on the time-frequency domain when the observed signal is a deterministic function plus additive stationary Gaussian noise. We derive their marginal and joint distributions, establish concentration inequalities that depend on the signal-to-noise ratio (SNR), and analyze their covariance structures. Based on these results, we derive an upper bound on the probability of incorrectly identifying the time-scale ridge of the clean signal, explore the regularity of scalogram contours, and study the relationship between AWT magnitude and phase. Our findings lay the groundwork for developing rigorous AWT-based algorithms in noisy environments.
{"title":"On Random Fields Associated With Analytic Wavelet Transform","authors":"Gi-Ren Liu;Yuan-Chung Sheu;Hau-Tieng Wu","doi":"10.1109/TIT.2026.3650970","DOIUrl":"https://doi.org/10.1109/TIT.2026.3650970","url":null,"abstract":"Despite the broad application of the analytic wavelet transform (AWT), a systematic statistical characterization of its magnitude and phase as inhomogeneous random fields on the time-frequency domain when the input is a random process remains underexplored. In this work, we study the magnitude and phase of the AWT as random fields on the time-frequency domain when the observed signal is a deterministic function plus additive stationary Gaussian noise. We derive their marginal and joint distributions, establish concentration inequalities that depend on the signal-to-noise ratio (SNR), and analyze their covariance structures. Based on these results, we derive an upper bound on the probability of incorrectly identifying the time-scale ridge of the clean signal, explore the regularity of scalogram contours, and study the relationship between AWT magnitude and phase. Our findings lay the groundwork for developing rigorous AWT-based algorithms in noisy environments.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"2005-2027"},"PeriodicalIF":2.9,"publicationDate":"2026-01-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216612","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 : 2025-12-31DOI: 10.1109/TIT.2025.3649987
Neha Sangwan;Varun Narayanan;Vinod M. Prabhakaran
We study communication with consensus over a broadcast channel—the receivers reliably decode the sender’s message when the sender is honest, and their decoder outputs agree even if the sender acts maliciously. We characterize the broadcast channels which permit this Byzantine consensus and determine their capacity. We show that communication with consensus is possible only when the broadcast channel has embedded in it a natural “common channel” whose output both receivers can unambiguously determine from their own channel outputs. Interestingly, in general, the consensus capacity may be larger than the point-to-point capacity of the common channel, i.e., while decoding, the receivers may make use of parts of their output signals on which they may not have consensus provided there are some parts (namely, the common channel output) on which they can agree.
{"title":"Consensus Capacity of Noisy Broadcast Channels","authors":"Neha Sangwan;Varun Narayanan;Vinod M. Prabhakaran","doi":"10.1109/TIT.2025.3649987","DOIUrl":"https://doi.org/10.1109/TIT.2025.3649987","url":null,"abstract":"We study communication with consensus over a broadcast channel—the receivers reliably decode the sender’s message when the sender is honest, and their decoder outputs agree even if the sender acts maliciously. We characterize the broadcast channels which permit this Byzantine consensus and determine their capacity. We show that communication with consensus is possible only when the broadcast channel has embedded in it a natural “common channel” whose output both receivers can unambiguously determine from their own channel outputs. Interestingly, in general, the consensus capacity may be larger than the point-to-point capacity of the common channel, i.e., while decoding, the receivers may make use of parts of their output signals on which they may not have consensus provided there are some parts (namely, the common channel output) on which they can agree.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"1874-1899"},"PeriodicalIF":2.9,"publicationDate":"2025-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216623","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 : 2025-12-30DOI: 10.1109/TIT.2025.3649596
Or Ordentlich;Yury Polyanskiy
Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language models), which is often bottlenecked by the speed of loading these matrices from memory. Unlike classical vector quantization and rate-distortion theory, the goal of these new compression algorithms is to be able to approximate not the matrices themselves, but their matrix product. Specifically, given a pair of real matrices $A,B$ an encoder (compressor) is applied to each of them independently producing descriptions with $R$ bits per entry. These representations subsequently are used by the decoder to estimate matrix product $A^{top } B$ . In this work, we provide a non-asymptotic lower bound on the mean squared error of this approximation (as a function of rate $R$ ) for the case of matrices $A,B$ with iid Gaussian entries. Algorithmically, we construct a universal quantizer based on nested lattices with an explicit guarantee of approximation error for any (non-random) pair of matrices $A$ , $B$ in terms of only Frobenius norms $|bar {A}|_{F}, |bar {B}|_{F}$ and $|bar {A}^{top } bar {B}|_{F}$ , where $bar {A},bar {B}$ are versions of $A,B$ with zero-centered columns, respectively. For iid Gaussian matrices our quantizer achieves the lower bound and is, thus, asymptotically optimal. A practical low-complexity version of our quantizer achieves performance quite close to optimal. In addition, we derive rate-distortion function for matrix multiplication of iid Gaussian matrices, which exhibits an interesting phase-transition at $Rapprox 0.906$ bit/entry, showing necessity of Johnson-Lindestrauss dimensionality reduction (sketching) in the low-rate regime.
{"title":"Optimal Quantization for Matrix Multiplication","authors":"Or Ordentlich;Yury Polyanskiy","doi":"10.1109/TIT.2025.3649596","DOIUrl":"https://doi.org/10.1109/TIT.2025.3649596","url":null,"abstract":"Recent work in machine learning community proposed multiple methods for performing lossy compression (quantization) of large matrices. This quantization is important for accelerating matrix multiplication (main component of large language models), which is often bottlenecked by the speed of loading these matrices from memory. Unlike classical vector quantization and rate-distortion theory, the goal of these new compression algorithms is to be able to approximate not the matrices themselves, but their matrix product. Specifically, given a pair of real matrices <inline-formula> <tex-math>$A,B$ </tex-math></inline-formula> an encoder (compressor) is applied to each of them independently producing descriptions with <inline-formula> <tex-math>$R$ </tex-math></inline-formula> bits per entry. These representations subsequently are used by the decoder to estimate matrix product <inline-formula> <tex-math>$A^{top } B$ </tex-math></inline-formula>. In this work, we provide a non-asymptotic lower bound on the mean squared error of this approximation (as a function of rate <inline-formula> <tex-math>$R$ </tex-math></inline-formula>) for the case of matrices <inline-formula> <tex-math>$A,B$ </tex-math></inline-formula> with iid Gaussian entries. Algorithmically, we construct a universal quantizer based on nested lattices with an explicit guarantee of approximation error for any (non-random) pair of matrices <inline-formula> <tex-math>$A$ </tex-math></inline-formula>, <inline-formula> <tex-math>$B$ </tex-math></inline-formula> in terms of only Frobenius norms <inline-formula> <tex-math>$|bar {A}|_{F}, |bar {B}|_{F}$ </tex-math></inline-formula> and <inline-formula> <tex-math>$|bar {A}^{top } bar {B}|_{F}$ </tex-math></inline-formula>, where <inline-formula> <tex-math>$bar {A},bar {B}$ </tex-math></inline-formula> are versions of <inline-formula> <tex-math>$A,B$ </tex-math></inline-formula> with zero-centered columns, respectively. For iid Gaussian matrices our quantizer achieves the lower bound and is, thus, asymptotically optimal. A practical low-complexity version of our quantizer achieves performance quite close to optimal. In addition, we derive rate-distortion function for matrix multiplication of iid Gaussian matrices, which exhibits an interesting phase-transition at <inline-formula> <tex-math>$Rapprox 0.906$ </tex-math></inline-formula> bit/entry, showing necessity of Johnson-Lindestrauss dimensionality reduction (sketching) in the low-rate regime.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 3","pages":"1943-1972"},"PeriodicalIF":2.9,"publicationDate":"2025-12-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146216619","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 : 2025-12-25DOI: 10.1109/TIT.2025.3648620
Éric Marchand;William E. Strawderman
For estimating the density of $Y|mu sim N_{d}(mu , nu I_{d})$ based on $X|mu sim N_{d}(mu , sigma ^{2}_{X} I_{d})$ with known $nu , sigma ^{2}_{X}$ , we consider the class $mathcal {P}$ of “extended plug-in” predictive densities $hat {q} sim N_{d}(hat {mu }, hat {nu } I_{d})$ . For a given prior density $pi $ for $mu $ and Kullback–Leibler loss, we investigate the optimal choice $hat {q}_{eb,pi }$ obtained by minimizing the expected posterior loss among $hat {q} in mathcal {P}$ , as initially proposed by Okudo and Komaki (2024). With $hat {q}_{eb,pi }$ having a simple form and a appealing alternative to the exact Bayesian predictive density, we investigate its Kullback–Leibler risk performance. Our main finding consists, for $d geq 3$ and a given superharmonic prior density $pi $ , in the determination of a lower cut-off point $bar {nu }$ such that $hat {q}_{eb,pi }$ dominates the benchmark minimum risk and minimax predictive density for $nu geq bar {nu }$ . Specific analyses are carried out and our results are illustrated for a pseudo-Bayes marginal density and a subclass of Strawderman prior densities.
{"title":"On Minimax Empirical Bayes Predictive Densities","authors":"Éric Marchand;William E. Strawderman","doi":"10.1109/TIT.2025.3648620","DOIUrl":"https://doi.org/10.1109/TIT.2025.3648620","url":null,"abstract":"For estimating the density of <inline-formula> <tex-math>$Y|mu sim N_{d}(mu , nu I_{d})$ </tex-math></inline-formula> based on <inline-formula> <tex-math>$X|mu sim N_{d}(mu , sigma ^{2}_{X} I_{d})$ </tex-math></inline-formula> with known <inline-formula> <tex-math>$nu , sigma ^{2}_{X}$ </tex-math></inline-formula>, we consider the class <inline-formula> <tex-math>$mathcal {P}$ </tex-math></inline-formula> of “extended plug-in” predictive densities <inline-formula> <tex-math>$hat {q} sim N_{d}(hat {mu }, hat {nu } I_{d})$ </tex-math></inline-formula>. For a given prior density <inline-formula> <tex-math>$pi $ </tex-math></inline-formula> for <inline-formula> <tex-math>$mu $ </tex-math></inline-formula> and Kullback–Leibler loss, we investigate the optimal choice <inline-formula> <tex-math>$hat {q}_{eb,pi }$ </tex-math></inline-formula> obtained by minimizing the expected posterior loss among <inline-formula> <tex-math>$hat {q} in mathcal {P}$ </tex-math></inline-formula>, as initially proposed by Okudo and Komaki (2024). With <inline-formula> <tex-math>$hat {q}_{eb,pi }$ </tex-math></inline-formula> having a simple form and a appealing alternative to the exact Bayesian predictive density, we investigate its Kullback–Leibler risk performance. Our main finding consists, for <inline-formula> <tex-math>$d geq 3$ </tex-math></inline-formula> and a given superharmonic prior density <inline-formula> <tex-math>$pi $ </tex-math></inline-formula>, in the determination of a lower cut-off point <inline-formula> <tex-math>$bar {nu }$ </tex-math></inline-formula> such that <inline-formula> <tex-math>$hat {q}_{eb,pi }$ </tex-math></inline-formula> dominates the benchmark minimum risk and minimax predictive density for <inline-formula> <tex-math>$nu geq bar {nu }$ </tex-math></inline-formula>. Specific analyses are carried out and our results are illustrated for a pseudo-Bayes marginal density and a subclass of Strawderman prior densities.","PeriodicalId":13494,"journal":{"name":"IEEE Transactions on Information Theory","volume":"72 2","pages":"1232-1239"},"PeriodicalIF":2.9,"publicationDate":"2025-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"146015950","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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