Information and Inference-A Journal of the Ima最新文献_第8页

Freeness over the diagonal and outliers detection in deformed random matrices with a variance profile 具有方差分布的变形随机矩阵中对角线上的自由度和异常值检测

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa012

Jérémie Bigot;Camille Male

{"title":"Freeness over the diagonal and outliers detection in deformed random matrices with a variance profile","authors":"Jérémie Bigot;Camille Male","doi":"10.1093/imaiai/iaaa012","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa012","url":null,"abstract":"We study the eigenvalue distribution of a Gaussian unitary ensemble (GUE) matrix with a variance profile that is perturbed by an additive random matrix that may possess spikes. Our approach is guided by Voiculescu's notion of freeness with amalgamation over the diagonal and by the notion of deterministic equivalent. This allows to derive a fixed point equation to approximate the spectral distribution of certain deformed GUE matrices with a variance profile and to characterize the location of potential outliers in such models in a non-asymptotic setting. We also consider the singular values distribution of a rectangular Gaussian random matrix with a variance profile in a similar setting of additive perturbation. We discuss the application of this approach to the study of low-rank matrix denoising models in the presence of heteroscedastic noise, that is when the amount of variance in the observed data matrix may change from entry to entry. Numerical experiments are used to illustrate our results. Deformed random matrix, Variance profile, Outlier detection, Free probability, Freeness with amalgamation, Operator-valued Stieltjes transform, Gaussian spiked model, Low-rank model. 2000 Math Subject Classification: 62G05, 62H12.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 3","pages":"863-919"},"PeriodicalIF":1.6,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa012","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50224073","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

Nonlinear generalization of the monotone single index model 单调单指标模型的非线性推广

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa013

Željko Kereta;Timo Klock;Valeriya Naumova

引用次数: 3

Approximate separability of symmetrically penalized least squares in high dimensions: characterization and consequences 高维对称惩罚最小二乘的近似可分性：特征和结果

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa037

Michael Celentano

{"title":"Approximate separability of symmetrically penalized least squares in high dimensions: characterization and consequences","authors":"Michael Celentano","doi":"10.1093/imaiai/iaaa037","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa037","url":null,"abstract":"We show that the high-dimensional behavior of symmetrically penalized least squares with a possibly non-separable, symmetric, convex penalty in both (i) the Gaussian sequence model and (ii) the linear model with uncorrelated Gaussian designs nearly agrees with the behavior of least squares with an appropriately chosen separable penalty in these same models. This agreement is established by finite-sample concentration inequalities which precisely characterize the behavior of symmetrically penalized least squares in both models via a comparison to a simple scalar statistical model. The concentration inequalities are novel in their precision and generality. Our results help clarify that the role non-separability can play in high-dimensional M-estimation. In particular, if the empirical distribution of the coordinates of the parameter is known—exactly or approximately—there are at most limited advantages to use non-separable, symmetric penalties over separable ones. In contrast, if the empirical distribution of the coordinates of the parameter is unknown, we argue that non-separable, symmetric penalties automatically implement an adaptive procedure, which we characterize. We also provide a partial converse which characterizes the adaptive procedures which can be implemented in this way.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 3","pages":"1105-1165"},"PeriodicalIF":1.6,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa037","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50347113","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: 3

Multi-reference factor analysis: low-rank covariance estimation under unknown translations 多参考因子分析：未知平移下的低秩协方差估计

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa019

Boris Landa;Yoel Shkolnisky

{"title":"Multi-reference factor analysis: low-rank covariance estimation under unknown translations","authors":"Boris Landa;Yoel Shkolnisky","doi":"10.1093/imaiai/iaaa019","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa019","url":null,"abstract":"We consider the problem of estimating the covariance matrix of a random signal observed through unknown translations (modeled by cyclic shifts) and corrupted by noise. Solving this problem allows to discover low-rank structures masked by the existence of translations (which act as nuisance parameters), with direct application to principal components analysis. We assume that the underlying signal is of length \u0000<tex>$L$</tex>\u0000 and follows a standard factor model with mean zero and \u0000<tex>$r$</tex>\u0000 normally distributed factors. To recover the covariance matrix in this case, we propose to employ the second- and fourth-order shift-invariant moments of the signal known as the power spectrum and the trispectrum. We prove that they are sufficient for recovering the covariance matrix (under a certain technical condition) when \u0000<tex>$r<sqrt{L}$</tex>\u0000. Correspondingly, we provide a polynomial-time procedure for estimating the covariance matrix from many (translated and noisy) observations, where no explicit knowledge of \u0000<tex>$r$</tex>\u0000 is required, and prove the procedure's statistical consistency. While our results establish that covariance estimation is possible from the power spectrum and the trispectrum for low-rank covariance matrices, we prove that this is not the case for full-rank covariance matrices. We conduct numerical experiments that corroborate our theoretical findings and demonstrate the favourable performance of our algorithms in various settings, including in high levels of noise.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 3","pages":"773-812"},"PeriodicalIF":1.6,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa019","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50224071","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: 3

The generalized orthogonal Procrustes problem in the high noise regime 高噪声环境下的广义正交Procrustes问题

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa035

Thomas Pumir;Amit Singer;Nicolas Boumal

引用次数: 19

Empirical risk minimization for dynamical systems and stationary processes 动力系统和平稳过程的经验风险最小化

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa043

Kevin McGoff;Andrew B Nobel

{"title":"Empirical risk minimization for dynamical systems and stationary processes","authors":"Kevin McGoff;Andrew B Nobel","doi":"10.1093/imaiai/iaaa043","DOIUrl":"https://doi.org/10.1093/imaiai/iaaa043","url":null,"abstract":"We introduce and analyze a general framework for empirical risk minimization in which the observations and models of interest may be stationary systems or processes. Within the framework, which is presented in terms of dynamical systems, empirical risk minimization can be studied as a two-step procedure in which (i) the trajectory of an observed (but unknown) system is fit by a trajectory of a known reference system via minimization of cumulative per-state loss, and (ii) an invariant parameter estimate is obtained from the initial state of the best fit trajectory. We show that the weak limits of the empirical measures of best-matched trajectories are dynamically invariant couplings (joinings) of the observed and reference systems with minimal risk. Moreover, we establish that the family of risk-minimizing joinings is convex and compact and that it fully characterizes the asymptotic behavior of the estimated parameters, directly addressing identifiability. Our analysis of empirical risk minimization applies to well-studied problems such as maximum likelihood estimation and non-linear regression, as well as more complex problems in which the models of interest are stationary processes. To illustrate the latter, we undertake an extended analysis of system identification from quantized trajectories subject to noise, a problem at the intersection of dynamics and statistics.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"10 3","pages":"1073-1104"},"PeriodicalIF":1.6,"publicationDate":"2021-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1093/imaiai/iaaa043","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50347112","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

Representation theoretic patterns in multi-frequency class averaging for three-dimensional cryo-electron microscopy 三维冷冻电子显微镜多频类平均中的表示论模式

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaab012

Yifeng Fan;Tingran Gao;Zhizhen Zhao

引用次数: 8

Multiplier bootstrap for quantile regression: non-asymptotic theory under random design 分位数回归的乘数自举：随机设计下的非渐近理论

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa006

Xiaoou Pan;Wen-Xin Zhou

引用次数: 9

Learning a deep convolutional neural network via tensor decomposition 通过张量分解学习深度卷积神经网络

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-02-01 DOI: 10.1093/imaiai/iaaa042

Samet Oymak;Mahdi Soltanolkotabi

引用次数: 4

Generalized score matching for general domains. 通用域的广义分数匹配。

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2021-01-25 eCollection Date: 2022-06-01 DOI: 10.1093/imaiai/iaaa041

Shiqing Yu, Mathias Drton, Ali Shojaie

引用次数: 16