Information and Inference-A Journal of the Ima最新文献_第3页

Generalization error bounds for iterative recovery algorithms unfolded as neural networks 迭代恢复算法的泛化误差边界以神经网络的形式展开

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad023

Ekkehard Schnoor, Arash Behboodi, Holger Rauhut

{"title":"Generalization error bounds for iterative recovery algorithms unfolded as neural networks","authors":"Ekkehard Schnoor, Arash Behboodi, Holger Rauhut","doi":"10.1093/imaiai/iaad023","DOIUrl":"https://doi.org/10.1093/imaiai/iaad023","url":null,"abstract":"Abstract Motivated by the learned iterative soft thresholding algorithm (LISTA), we introduce a general class of neural networks suitable for sparse reconstruction from few linear measurements. By allowing a wide range of degrees of weight-sharing between the flayers, we enable a unified analysis for very different neural network types, ranging from recurrent ones to networks more similar to standard feedforward neural networks. Based on training samples, via empirical risk minimization, we aim at learning the optimal network parameters and thereby the optimal network that reconstructs signals from their low-dimensional linear measurements. We derive generalization bounds by analyzing the Rademacher complexity of hypothesis classes consisting of such deep networks, that also take into account the thresholding parameters. We obtain estimates of the sample complexity that essentially depend only linearly on the number of parameters and on the depth. We apply our main result to obtain specific generalization bounds for several practical examples, including different algorithms for (implicit) dictionary learning, and convolutional neural networks.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136266735","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Separation-free super-resolution from compressed measurements is possible: an orthonormal atomic norm minimization approach 从压缩测量中实现无分离的超分辨率是可能的:一种标准正交原子范数最小化方法

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad033

Jirong Yi, Soura Dasgupta, Jian-Feng Cai, Mathews Jacob, Jingchao Gao, Myung Cho, Weiyu Xu

{"title":"Separation-free super-resolution from compressed measurements is possible: an orthonormal atomic norm minimization approach","authors":"Jirong Yi, Soura Dasgupta, Jian-Feng Cai, Mathews Jacob, Jingchao Gao, Myung Cho, Weiyu Xu","doi":"10.1093/imaiai/iaad033","DOIUrl":"https://doi.org/10.1093/imaiai/iaad033","url":null,"abstract":"Abstract We consider the problem of recovering the superposition of $R$ distinct complex exponential functions from compressed non-uniform time-domain samples. Total variation (TV) minimization or atomic norm minimization was proposed in the literature to recover the $R$ frequencies or the missing data. However, it is known that in order for TV minimization and atomic norm minimization to recover the missing data or the frequencies, the underlying $R$ frequencies are required to be well separated, even when the measurements are noiseless. This paper shows that the Hankel matrix recovery approach can super-resolve the $R$ complex exponentials and their frequencies from compressed non-uniform measurements, regardless of how close their frequencies are to each other. We propose a new concept of orthonormal atomic norm minimization (OANM), and demonstrate that the success of Hankel matrix recovery in separation-free super-resolution comes from the fact that the nuclear norm of a Hankel matrix is an orthonormal atomic norm. More specifically, we show that, in traditional atomic norm minimization, the underlying parameter values must be well separated to achieve successful signal recovery, if the atoms are changing continuously with respect to the continuously valued parameter. In contrast, for the OANM, it is possible the OANM is successful even though the original atoms can be arbitrarily close. As a byproduct of this research, we provide one matrix-theoretic inequality of nuclear norm, and give its proof using the theory of compressed sensing.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136266739","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Minimax detection of localized signals in statistical inverse problems 统计逆问题中局域信号的极大极小检测

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad026

Markus Pohlmann, Frank Werner, Axel Munk

引用次数: 0

Sharp, strong and unique minimizers for low complexity robust recovery 锐利，强大和独特的最小化低复杂性稳健恢复

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-23 DOI: 10.1093/imaiai/iaad005

Jalal Fadili, Tran T. A. Nghia, Trinh T. T. Tran

引用次数: 0

Non-adaptive algorithms for threshold group testing with consecutive positives 连续阳性阈值组检测的非自适应算法

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-04 DOI: 10.1093/imaiai/iaad009

{"title":"Non-adaptive algorithms for threshold group testing with consecutive positives","authors":"","doi":"10.1093/imaiai/iaad009","DOIUrl":"https://doi.org/10.1093/imaiai/iaad009","url":null,"abstract":"\u0000 Given up to $d$ positive items in a large population of $n$ items ($d ll n$), the goal of threshold group testing is to efficiently identify the positives via tests, where a test on a subset of items is positive if the subset contains at least $u$ positive items, negative if it contains up to $ell $ positive items and arbitrary (either positive or negative) otherwise. The parameter $g = u - ell - 1$ is called the gap. In non-adaptive strategies, all tests are fixed in advance and can be represented as a measurement matrix, in which each row and column represent a test and an item, respectively. In this paper, we consider non-adaptive threshold group testing with consecutive positives in which the items are linearly ordered and the positives are consecutive in that order. We show that by designing deterministic and strongly explicit measurement matrices, $lceil log _{2}{lceil frac {n}{d} rceil } rceil + 2d + 3$ (respectively, $lceil log _{2}{lceil frac {n}{d} rceil } rceil + 3d$) tests suffice to identify the positives in $O left ( log _{2}{frac {n}{d}} + d right )$ time when $g = 0$ (respectively, $g> 0$). The results significantly improve the state-of-the-art scheme that needs $15 lceil log _{2}{lceil frac {n}{d} rceil } rceil + 4d + 71$ tests to identify the positives in $O left ( frac {n}{d} log _{2}{frac {n}{d}} + ud^{2} right )$ time, and whose associated measurement matrices are random and (non-strongly) explicit.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74278014","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Theoretical analysis and computation of the sample Fréchet mean of sets of large graphs for various metrics 各种指标的大图集样本均值的理论分析与计算

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-03-28 DOI: 10.1093/imaiai/iaad002

Daniel Ferguson, F. G. Meyer

引用次数: 0

Local Viterbi property in decoding 译码中的局部维特比特性

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-03-20 DOI: 10.1093/imaiai/iaad004

J. Lember

{"title":"Local Viterbi property in decoding","authors":"J. Lember","doi":"10.1093/imaiai/iaad004","DOIUrl":"https://doi.org/10.1093/imaiai/iaad004","url":null,"abstract":"\u0000 The article studies the decoding problem (also known as the classification or the segmentation problem) with pairwise Markov models (PMMs). A PMM is a process where the observation process and the underlying state sequence form a two-dimensional Markov chain, a natural generalization of hidden Markov model. The standard solutions to the decoding problem are the so-called Viterbi path—a sequence with maximum state path probability given the observations—or the pointwise maximum a posteriori (PMAP) path that maximizes the expected number of correctly classified entries. When the goal is to simultaneously maximize both criterions—conditional probability (corresponding to Viterbi path) and pointwise conditional probability (corresponding to PMAP path)—then they are combined into one single criterion via the regularization parameter $C$. The main objective of the article is to study the behaviour of the solution—called the hybrid path—as $C$ grows. Increasing $C$ increases the conditional probability of the hybrid path and when $C$ is big enough then every hybrid path is a Viterbi path. We show that hybrid paths also approach the Viterbi path locally: we define $m$-locally Viterbi paths and show that the hybrid path is $m$-locally Viterbi whenever $C$ is big enough. This all might lead to an impression that when $C$ is relatively big then any hybrid path that is not yet Viterbi differs from the Viterbi path by a few single entries only. We argue that this intuition is wrong, because when unique and $m$-locally Viterbi, then different hybrid paths differ by at least $m$ entries. Thus, when $C$ increases then the different hybrid paths tend to differ from each other by larger and larger intervals. Hence the hybrid paths might offer a variety of rather different solutions to the decoding problem.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.6,"publicationDate":"2023-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82746142","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Minimum probability of error of list M-ary hypothesis testing 列表m -玛利假设检验的最小误差概率

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-02-27 DOI: 10.1093/imaiai/iaad001

Ehsan Asadi Kangarshahi, A. Guillén i Fàbregas

引用次数: 0

A unifying view of modal clustering 模态聚类的统一观点

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-08-01 DOI: 10.1093/imaiai/iaac030

Ery Arias-Castro;Wanli Qiao

引用次数: 0

On sharp stochastic zeroth-order Hessian estimators over Riemannian manifolds 关于黎曼流形上的零阶随机Hessian估计

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-08-01 DOI: 10.1093/imaiai/iaac027

Tianyu Wang

引用次数: 0