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Information and Inference-A Journal of the Ima最新文献

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OUP accepted manuscript OUP接受稿件
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2021-01-01 DOI: 10.1093/imaiai/iaab021
{"title":"OUP accepted manuscript","authors":"","doi":"10.1093/imaiai/iaab021","DOIUrl":"https://doi.org/10.1093/imaiai/iaab021","url":null,"abstract":"","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"63 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84732722","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
Concentration inequalities for the empirical distribution of discrete distributions: beyond the method of types 离散分布的经验分布的集中不等式:超越类型的方法
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-12-16 DOI: 10.1093/imaiai/iaz025
Jay Mardia, Jiantao Jiao, Ervin Tánczos, R. Nowak, T. Weissman
{"title":"Concentration inequalities for the empirical distribution of discrete distributions: beyond the method of types","authors":"Jay Mardia, Jiantao Jiao, Ervin Tánczos, R. Nowak, T. Weissman","doi":"10.1093/imaiai/iaz025","DOIUrl":"https://doi.org/10.1093/imaiai/iaz025","url":null,"abstract":"We study concentration inequalities for the Kullback–Leibler (KL) divergence between the empirical distribution and the true distribution. Applying a recursion technique, we improve over the method of types bound uniformly in all regimes of sample size n and alphabet size k, and the improvement becomes more significant when k is large. We discuss the applications of our results in obtaining tighter concentration inequalities for L1 deviations of the empirical distribution from the true distribution, and the difference between concentration around the expectation or zero. We also obtain asymptotically tight bounds on the variance of the KL divergence between the empirical and true distribution, and demonstrate their quantitatively different behaviors between small and large sample sizes compared to the alphabet size.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"9 1","pages":"813-850"},"PeriodicalIF":1.6,"publicationDate":"2020-12-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87011039","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: 29
Analysis of fast structured dictionary learning. 快速结构化词典学习分析
IF 1.4 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-12-01 Epub Date: 2019-11-19 DOI: 10.1093/imaiai/iaz028
Saiprasad Ravishankar, Anna Ma, Deanna Needell
{"title":"Analysis of fast structured dictionary learning.","authors":"Saiprasad Ravishankar, Anna Ma, Deanna Needell","doi":"10.1093/imaiai/iaz028","DOIUrl":"10.1093/imaiai/iaz028","url":null,"abstract":"<p><p>Sparsity-based models and techniques have been exploited in many signal processing and imaging applications. Data-driven methods based on dictionary and sparsifying transform learning enable learning rich image features from data and can outperform analytical models. In particular, alternating optimization algorithms have been popular for learning such models. In this work, we focus on alternating minimization for a specific structured unitary sparsifying operator learning problem and provide a convergence analysis. While the algorithm converges to the critical points of the problem generally, our analysis establishes under mild assumptions, the local linear convergence of the algorithm to the underlying sparsifying model of the data. Analysis and numerical simulations show that our assumptions hold for standard probabilistic data models. In practice, the algorithm is robust to initialization.</p>","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"9 4","pages":"785-811"},"PeriodicalIF":1.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7737167/pdf/iaz028.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38730960","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Matchability of heterogeneous networks pairs. 异构网络对的匹配性。
IF 1.4 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-12-01 Epub Date: 2020-01-06 DOI: 10.1093/imaiai/iaz031
Vince Lyzinski, Daniel L Sussman
{"title":"Matchability of heterogeneous networks pairs.","authors":"Vince Lyzinski, Daniel L Sussman","doi":"10.1093/imaiai/iaz031","DOIUrl":"10.1093/imaiai/iaz031","url":null,"abstract":"<p><p>We consider the problem of graph matchability in non-identically distributed networks. In a general class of edge-independent networks, we demonstrate that graph matchability can be lost with high probability when matching the networks directly. We further demonstrate that under mild model assumptions, matchability is almost perfectly recovered by centering the networks using universal singular value thresholding before matching. These theoretical results are then demonstrated in both real and synthetic simulation settings. We also recover analogous core-matchability results in a very general core-junk network model, wherein some vertices do not correspond between the graph pair.</p>","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"9 4","pages":"749-783"},"PeriodicalIF":1.4,"publicationDate":"2020-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7737166/pdf/iaz031.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"38730959","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Overlap matrix concentration in optimal Bayesian inference 最优贝叶斯推理中的重叠矩阵集中
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-10-01 DOI: 10.1093/imaiai/iaaa008
Jean Barbier
{"title":"Overlap matrix concentration in optimal Bayesian inference","authors":"Jean Barbier","doi":"10.1093/imaiai/iaaa008","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa008","url":null,"abstract":"We consider models of Bayesian inference of signals with vectorial components of finite dimensionality. We show that under a proper perturbation, these models are replica symmetric in the sense that the overlap matrix concentrates. The overlap matrix is the order parameter in these models and is directly related to error metrics such as minimum mean-square errors. Our proof is valid in the optimal Bayesian inference setting. This means that it relies on the assumption that the model and all its hyper-parameters are known so that the posterior distribution can be written exactly. Examples of important problems in high-dimensional inference and learning to which our results apply are low-rank tensor factorization, the committee machine neural network with a finite number of hidden neurons in the teacher–student scenario or multi-layer versions of the generalized linear model.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 1","pages":"597-623"},"PeriodicalIF":1.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50262519","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: 23
Tight recovery guarantees for orthogonal matching pursuit under Gaussian noise 高斯噪声下正交匹配追踪的严密恢复保证
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-10-01 DOI: 10.1093/imaiai/iaaa021
Chen Amiraz;Robert Krauthgamer;Boaz Nadler
{"title":"Tight recovery guarantees for orthogonal matching pursuit under Gaussian noise","authors":"Chen Amiraz;Robert Krauthgamer;Boaz Nadler","doi":"10.1093/imaiai/iaaa021","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa021","url":null,"abstract":"Orthogonal matching pursuit (OMP) is a popular algorithm to estimate an unknown sparse vector from multiple linear measurements of it. Assuming exact sparsity and that the measurements are corrupted by additive Gaussian noise, the success of OMP is often formulated as exactly recovering the support of the sparse vector. Several authors derived a sufficient condition for exact support recovery by OMP with high probability depending on the signal-to-noise ratio, defined as the magnitude of the smallest non-zero coefficient of the vector divided by the noise level. We make two contributions. First, we derive a slightly sharper sufficient condition for two variants of OMP, in which either the sparsity level or the noise level is known. Next, we show that this sharper sufficient condition is tight, in the following sense: for a wide range of problem parameters, there exist a dictionary of linear measurements and a sparse vector with a signal-to-noise ratio slightly below that of the sufficient condition, for which with high probability OMP fails to recover its support. Finally, we present simulations that illustrate that our condition is tight for a much broader range of dictionaries.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 1","pages":"573-595"},"PeriodicalIF":1.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa021","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50262615","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: 4
Erratum to: Super-resolution of near-colliding point sources 勘误表：近碰撞点源的超分辨率
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-10-01 DOI: 10.1093/imaiai/iaaa015
Dmitry Batenkov;Gil Goldman;Yosef Yomdin
{"title":"Erratum to: Super-resolution of near-colliding point sources","authors":"Dmitry Batenkov;Gil Goldman;Yosef Yomdin","doi":"10.1093/imaiai/iaaa015","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa015","url":null,"abstract":"","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 1","pages":"721-721"},"PeriodicalIF":1.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50262522","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
The limits of distribution-free conditional predictive inference 无分布条件预测推理的极限
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-10-01 DOI: 10.1093/imaiai/iaaa017
Rina Foygel Barber;Emmanuel J Candès;Aaditya Ramdas;Ryan J Tibshirani
{"title":"The limits of distribution-free conditional predictive inference","authors":"Rina Foygel Barber;Emmanuel J Candès;Aaditya Ramdas;Ryan J Tibshirani","doi":"10.1093/imaiai/iaaa017","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa017","url":null,"abstract":"We consider the problem of distribution-free predictive inference, with the goal of producing predictive coverage guarantees that hold conditionally rather than marginally. Existing methods such as conformal prediction offer marginal coverage guarantees, where predictive coverage holds on average over all possible test points, but this is not sufficient for many practical applications where we would like to know that our predictions are valid for a given individual, not merely on average over a population. On the other hand, exact conditional inference guarantees are known to be impossible without imposing assumptions on the underlying distribution. In this work, we aim to explore the space in between these two and examine what types of relaxations of the conditional coverage property would alleviate some of the practical concerns with marginal coverage guarantees while still being possible to achieve in a distribution-free setting.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 1","pages":"455-482"},"PeriodicalIF":1.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa017","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50262612","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: 162
Oracle inequalities for square root analysis estimators with application to total variation penalties 平方根分析估计量的Oracle不等式及其在总变异罚中的应用
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-10-01 DOI: 10.1093/imaiai/iaaa002
Francesco Ortelli;Sara van de Geer
{"title":"Oracle inequalities for square root analysis estimators with application to total variation penalties","authors":"Francesco Ortelli;Sara van de Geer","doi":"10.1093/imaiai/iaaa002","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa002","url":null,"abstract":"Through the direct study of the analysis estimator we derive oracle inequalities with fast and slow rates by adapting the arguments involving projections by Dalalyan et al. (2017, Bernoulli, 23, 552–581). We then extend the theory to the square root analysis estimator. Finally, we focus on (square root) total variation regularized estimators on graphs and obtain constant-friendly rates, which, up to log terms, match previous results obtained by entropy calculations. We also obtain an oracle inequality for the (square root) total variation regularized estimator over the cycle graph.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 1","pages":"483-514"},"PeriodicalIF":1.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50262613","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: 6
Composite optimization for robust rank one bilinear sensing 鲁棒秩一双线性传感的复合优化
IF 1.6 4区 数学
Information and Inference-A Journal of the Ima Pub Date : 2020-10-01 DOI: 10.1093/imaiai/iaaa027
Vasileios Charisopoulos;Damek Davis;Mateo Díaz;Dmitriy Drusvyatskiy
{"title":"Composite optimization for robust rank one bilinear sensing","authors":"Vasileios Charisopoulos;Damek Davis;Mateo Díaz;Dmitriy Drusvyatskiy","doi":"10.1093/imaiai/iaaa027","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa027","url":null,"abstract":"We consider the task of recovering a pair of vectors from a set of rank one bilinear measurements, possibly corrupted by noise. Most notably, the problem of robust blind deconvolution can be modeled in this way. We consider a natural nonsmooth formulation of the rank one bilinear sensing problem and show that its moduli of weak convexity, sharpness and Lipschitz continuity are all dimension independent, under favorable statistical assumptions. This phenomenon persists even when up to half of the measurements are corrupted by noise. Consequently, standard algorithms, such as the subgradient and prox-linear methods, converge at a rapid dimension-independent rate when initialized within a constant relative error of the solution. We complete the paper with a new initialization strategy, complementing the local search algorithms. The initialization procedure is both provably efficient and robust to outlying measurements. Numerical experiments, on both simulated and real data, illustrate the developed theory and methods.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 1","pages":"333-396"},"PeriodicalIF":1.6,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa027","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50262610","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: 4
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