Information and Inference-A Journal of the Ima最新文献_第5页

Nearly minimax-optimal rates for noisy sparse phase retrieval via early-stopped mirror descent 基于早期停止镜像下降的噪声稀疏相位检索的近似极小极大最优速率

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-08-01 DOI: 10.1093/imaiai/iaac024

Fan Wu;Patrick Rebeschini

{"title":"Nearly minimax-optimal rates for noisy sparse phase retrieval via early-stopped mirror descent","authors":"Fan Wu;Patrick Rebeschini","doi":"10.1093/imaiai/iaac024","DOIUrl":"https://doi.org/10.1093/imaiai/iaac024","url":null,"abstract":"This paper studies early-stopped mirror descent applied to noisy sparse phase retrieval, which is the problem of recovering a \u0000<tex>$k$</tex>\u0000-sparse signal \u0000<tex>$textbf{x}^star in{mathbb{R}}^n$</tex>\u0000 from a set of quadratic Gaussian measurements corrupted by sub-exponential noise. We consider the (non-convex) unregularized empirical risk minimization problem and show that early-stopped mirror descent, when equipped with the hypentropy mirror map and proper initialization, achieves a nearly minimax-optimal rate of convergence, provided the sample size is at least of order \u0000<tex>$k^2$</tex>\u0000 (modulo logarithmic term) and the minimum (in modulus) non-zero entry of the signal is on the order of \u0000<tex>$|textbf{x}^star |_2/sqrt{k}$</tex>\u0000. Our theory leads to a simple algorithm that does not rely on explicit regularization or thresholding steps to promote sparsity. More generally, our results establish a connection between mirror descent and sparsity in the non-convex problem of noisy sparse phase retrieval, adding to the literature on early stopping that has mostly focused on non-sparse, Euclidean and convex settings via gradient descent. Our proof combines a potential-based analysis of mirror descent with a quantitative control on a variational coherence property that we establish along the path of mirror descent, up to a prescribed stopping time.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"12 2","pages":"633-713"},"PeriodicalIF":1.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016800/10058586/10058608.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50297616","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

Perturbation bounds for (nearly) orthogonally decomposable tensors with statistical applications （近似）正交可分解张量的扰动界及其统计应用

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-08-01 DOI: 10.1093/imaiai/iaac033

Arnab Auddy;Ming Yuan

引用次数: 0

Breaking the sample complexity barrier to regret-optimal model-free reinforcement learning 打破样本复杂性障碍后悔最优无模型强化学习

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-08-01 DOI: 10.1093/imaiai/iaac034

Gen Li;Laixi Shi;Yuxin Chen;Yuejie Chi

{"title":"Breaking the sample complexity barrier to regret-optimal model-free reinforcement learning","authors":"Gen Li;Laixi Shi;Yuxin Chen;Yuejie Chi","doi":"10.1093/imaiai/iaac034","DOIUrl":"https://doi.org/10.1093/imaiai/iaac034","url":null,"abstract":"Achieving sample efficiency in online episodic reinforcement learning (RL) requires optimally balancing exploration and exploitation. When it comes to a finite-horizon episodic Markov decision process with \u0000<tex>$S$</tex>\u0000 states, \u0000<tex>$A$</tex>\u0000 actions and horizon length \u0000<tex>$H$</tex>\u0000, substantial progress has been achieved toward characterizing the minimax-optimal regret, which scales on the order of \u0000<tex>$sqrt{H^2SAT}$</tex>\u0000 (modulo log factors) with \u0000<tex>$T$</tex>\u0000 the total number of samples. While several competing solution paradigms have been proposed to minimize regret, they are either memory-inefficient, or fall short of optimality unless the sample size exceeds an enormous threshold (e.g. \u0000<tex>$S^6A^4 ,mathrm{poly}(H)$</tex>\u0000 for existing model-free methods).To overcome such a large sample size barrier to efficient RL, we design a novel model-free algorithm, with space complexity \u0000<tex>$O(SAH)$</tex>\u0000, that achieves near-optimal regret as soon as the sample size exceeds the order of \u0000<tex>$SA,mathrm{poly}(H)$</tex>\u0000. In terms of this sample size requirement (also referred to the initial burn-in cost), our method improves—by at least a factor of \u0000<tex>$S^5A^3$</tex>\u0000—upon any prior memory-efficient algorithm that is asymptotically regret-optimal. Leveraging the recently introduced variance reduction strategy (also called reference-advantage decomposition), the proposed algorithm employs an early-settled reference update rule, with the aid of two Q-learning sequences with upper and lower confidence bounds. The design principle of our early-settled variance reduction method might be of independent interest to other RL settings that involve intricate exploration–exploitation trade-offs.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"12 2","pages":"969-1043"},"PeriodicalIF":1.6,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://ieeexplore.ieee.org/iel7/8016800/10058586/10058618.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"50298054","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: 35

Dynamic ranking and translation synchronization 动态排序和翻译同步

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-07-04 DOI: 10.1093/imaiai/iaad029

E. Araya, Eglantine Karl'e, Hemant Tyagi

{"title":"Dynamic ranking and translation synchronization","authors":"E. Araya, Eglantine Karl'e, Hemant Tyagi","doi":"10.1093/imaiai/iaad029","DOIUrl":"https://doi.org/10.1093/imaiai/iaad029","url":null,"abstract":"\u0000 In many applications, such as sport tournaments or recommendation systems, we have at our disposal data consisting of pairwise comparisons between a set of $n$ items (or players). The objective is to use these data to infer the latent strength of each item and/or their ranking. Existing results for this problem predominantly focus on the setting consisting of a single comparison graph $G$. However, there exist scenarios (e.g. sports tournaments) where the pairwise comparison data evolve with time. Theoretical results for this dynamic setting are relatively limited, and are the focus of this paper. We study an extension of the translation synchronization problem, to the dynamic setting. In this set-up, we are given a sequence of comparison graphs $(G_t)_{tin{{mathscr{T}}}}$, where $ {{mathscr{T}}} subset [0,1]$ is a grid representing the time domain, and for each item $i$ and time $tin{{mathscr{T}}}$ there is an associated unknown strength parameter $z^*_{t,i}in{{mathbb{R}}}$. We aim to recover, for $tin{{mathscr{T}}}$, the strength vector $z^*_t=(z^*_{t,1},dots ,z^*_{t,n})$ from noisy measurements of $z^*_{t,i}-z^*_{t,j}$, where $left {{i,j}right }$ is an edge in $G_t$. Assuming that $z^*_t$ evolves smoothly in $t$, we propose two estimators—one based on a smoothness-penalized least squares approach and the other based on projection onto the low-frequency eigenspace of a suitable smoothness operator. For both estimators, we provide finite sample bounds for the $ell _2$ estimation error under the assumption that $G_t$ is connected for all $tin{{mathscr{T}}}$, thus proving the consistency of the proposed methods in terms of the grid size $|mathscr{T}|$. We complement our theoretical findings with experiments on synthetic and real data.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"8 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82565710","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

Super-resolution multi-reference alignment. 超分辨率多参考对齐。

IF 1.4 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-06-01 Epub Date: 2021-02-18 DOI: 10.1093/imaiai/iaab003

Tamir Bendory, Ariel Jaffe, William Leeb, Nir Sharon, Amit Singer

引用次数: 0

Minimax optimal clustering of bipartite graphs with a generalized power method 二部图的极小极大最优聚类的广义幂方法

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-05-24 DOI: 10.1093/imaiai/iaad006

Guillaume Braun, Hemant Tyagi

{"title":"Minimax optimal clustering of bipartite graphs with a generalized power method","authors":"Guillaume Braun, Hemant Tyagi","doi":"10.1093/imaiai/iaad006","DOIUrl":"https://doi.org/10.1093/imaiai/iaad006","url":null,"abstract":"\u0000 Clustering bipartite graphs is a fundamental task in network analysis. In the high-dimensional regime where the number of rows $n_{1}$ and the number of columns $n_{2}$ of the associated adjacency matrix are of different order, the existing methods derived from the ones used for symmetric graphs can come with sub-optimal guarantees. Due to increasing number of applications for bipartite graphs in the high-dimensional regime, it is of fundamental importance to design optimal algorithms for this setting. The recent work of Ndaoud et al. (2022, IEEE Trans. Inf. Theory, 68, 1960–1975) improves the existing upper-bound for the misclustering rate in the special case where the columns (resp. rows) can be partitioned into $L = 2$ (resp. $K = 2$) communities. Unfortunately, their algorithm cannot be extended to the more general setting where $K neq L geq 2$. We overcome this limitation by introducing a new algorithm based on the power method. We derive conditions for exact recovery in the general setting where $K neq L geq 2$, and show that it recovers the result in Ndaoud et al. (2022, IEEE Trans. Inf. Theory, 68, 1960–1975). We also derive a minimax lower bound on the misclustering error when $K=L$ under a symmetric version of our model, which matches the corresponding upper bound up to a factor depending on $K$.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"57 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74089679","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: 5

An analysis of classical multidimensional scaling with applications to clustering. 经典多维尺度分析与聚类应用。

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-04-23 eCollection Date: 2023-03-01 DOI: 10.1093/imaiai/iaac004

Anna Little, Yuying Xie, Qiang Sun

引用次数: 0

Linear convergence of the subspace constrained mean shift algorithm: from Euclidean to directional data. 子空间约束均值移动算法的线性收敛：从欧几里得数据到方向数据。

IF 1.4 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-04-09 eCollection Date: 2023-03-01 DOI: 10.1093/imaiai/iaac005

Yikun Zhang, Yen-Chi Chen

引用次数: 0

Zero-truncated Poisson regression for sparse multiway count data corrupted by false zeros 被假零损坏的稀疏多路计数数据的零截断泊松回归

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2022-01-25 DOI: 10.1093/imaiai/iaad016

Oscar L'opez, Daniel M. Dunlavy, R. Lehoucq

{"title":"Zero-truncated Poisson regression for sparse multiway count data corrupted by false zeros","authors":"Oscar L'opez, Daniel M. Dunlavy, R. Lehoucq","doi":"10.1093/imaiai/iaad016","DOIUrl":"https://doi.org/10.1093/imaiai/iaad016","url":null,"abstract":"\u0000 We propose a novel statistical inference methodology for multiway count data that is corrupted by false zeros that are indistinguishable from true zero counts. Our approach consists of zero-truncating the Poisson distribution to neglect all zero values. This simple truncated approach dispenses with the need to distinguish between true and false zero counts and reduces the amount of data to be processed. Inference is accomplished via tensor completion that imposes low-rank tensor structure on the Poisson parameter space. Our main result shows that an $N$-way rank-$R$ parametric tensor $boldsymbol{mathscr{M}}in (0,infty )^{Itimes cdots times I}$ generating Poisson observations can be accurately estimated by zero-truncated Poisson regression from approximately $IR^2log _2^2(I)$ non-zero counts under the nonnegative canonical polyadic decomposition. Our result also quantifies the error made by zero-truncating the Poisson distribution when the parameter is uniformly bounded from below. Therefore, under a low-rank multiparameter model, we propose an implementable approach guaranteed to achieve accurate regression in under-determined scenarios with substantial corruption by false zeros. Several numerical experiments are presented to explore the theoretical results.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":"14 1","pages":""},"PeriodicalIF":1.6,"publicationDate":"2022-01-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89460693","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

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 : 2022-01-01 DOI: 10.1093/imaiai/iaac007

引用次数: 0