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

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":null,"pages":null},"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":null,"pages":null},"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 1.4 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":null,"pages":null},"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/iaac012

引用次数: 0

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

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/iaac008

引用次数: 0

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/iaac011

引用次数: 0