Information and Inference-A Journal of the Ima最新文献_第2页

Spectral top-down recovery of latent tree models. 潜在树模型的光谱自上而下复原。

IF 1.4 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-08-16 eCollection Date: 2023-09-01 DOI: 10.1093/imaiai/iaad032

Yariv Aizenbud, Ariel Jaffe, Meng Wang, Amber Hu, Noah Amsel, Boaz Nadler, Joseph T Chang, Yuval Kluger

{"title":"Spectral top-down recovery of latent tree models.","authors":"Yariv Aizenbud, Ariel Jaffe, Meng Wang, Amber Hu, Noah Amsel, Boaz Nadler, Joseph T Chang, Yuval Kluger","doi":"10.1093/imaiai/iaad032","DOIUrl":"10.1093/imaiai/iaad032","url":null,"abstract":"Modeling the distribution of high-dimensional data by a latent tree graphical model is a prevalent approach in multiple scientific domains. A common task is to infer the underlying tree structure, given only observations of its terminal nodes. Many algorithms for tree recovery are computationally intensive, which limits their applicability to trees of moderate size. For large trees, a common approach, termed divide-and-conquer, is to recover the tree structure in two steps. First, separately recover the structure of multiple, possibly random subsets of the terminal nodes. Second, merge the resulting subtrees to form a full tree. Here, we develop spectral top-down recovery (STDR), a deterministic divide-and-conquer approach to infer large latent tree models. Unlike previous methods, STDR partitions the terminal nodes in a non random way, based on the Fiedler vector of a suitable Laplacian matrix related to the observed nodes. We prove that under certain conditions, this partitioning is consistent with the tree structure. This, in turn, leads to a significantly simpler merging procedure of the small subtrees. We prove that STDR is statistically consistent and bound the number of samples required to accurately recover the tree with high probability. Using simulated data from several common tree models in phylogenetics, we demonstrate that STDR has a significant advantage in terms of runtime, with improved or similar accuracy.","PeriodicalId":45437,"journal":{"name":"Information and Inference-A Journal of the Ima","volume":null,"pages":null},"PeriodicalIF":1.4,"publicationDate":"2023-08-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10431953/pdf/","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"10233338","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

Minimax optimal regression over Sobolev spaces via Laplacian Eigenmaps on neighbourhood graphs 邻域图上拉普拉斯特征映射在Sobolev空间上的极大极小最优回归

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad034

Alden Green, Sivaraman Balakrishnan, Ryan J Tibshirani

{"title":"Minimax optimal regression over Sobolev spaces via Laplacian Eigenmaps on neighbourhood graphs","authors":"Alden Green, Sivaraman Balakrishnan, Ryan J Tibshirani","doi":"10.1093/imaiai/iaad034","DOIUrl":"https://doi.org/10.1093/imaiai/iaad034","url":null,"abstract":"Abstract In this paper, we study the statistical properties of Principal Components Regression with Laplacian Eigenmaps (PCR-LE), a method for non-parametric regression based on Laplacian Eigenmaps (LE). PCR-LE works by projecting a vector of observed responses ${textbf Y} = (Y_1,ldots ,Y_n)$ onto a subspace spanned by certain eigenvectors of a neighbourhood graph Laplacian. We show that PCR-LE achieves minimax rates of convergence for random design regression over Sobolev spaces. Under sufficient smoothness conditions on the design density $p$, PCR-LE achieves the optimal rates for both estimation (where the optimal rate in squared $L^2$ norm is known to be $n^{-2s/(2s + d)}$) and goodness-of-fit testing ($n^{-4s/(4s + d)}$). We also consider the situation where the design is supported on a manifold of small intrinsic dimension $m$, and give upper bounds establishing that PCR-LE achieves the faster minimax estimation ($n^{-2s/(2s + m)}$) and testing ($n^{-4s/(4s + m)}$) rates of convergence. Interestingly, these rates are almost always much faster than the known rates of convergence of graph Laplacian eigenvectors to their population-level limits; in other words, for this problem regression with estimated features appears to be much easier, statistically speaking, than estimating the features itself. We support these theoretical results with empirical evidence.","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":"136266565","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

Statistical characterization of the chordal product determinant of Grassmannian codes 格拉斯曼码弦积行列式的统计表征

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad035

Javier Álvarez-Vizoso, Carlos Beltrán, Diego Cuevas, Ignacio Santamaría, Vít Tuček, Gunnar Peters

引用次数: 0

Analysis of the ratio of ℓ1 and ℓ2 norms for signal recovery with partial support information 具有部分支持信息的信号恢复的1和2范数之比分析

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad015

Huanmin Ge, Wengu Chen, Michael K. Ng

引用次数: 1

Approximately low-rank recovery from noisy and local measurements by convex program 用凸规划从噪声和局部测量中近似低秩恢复

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad013

Kiryung Lee, Rakshith Sharma Srinivasa, Marius Junge, Justin Romberg

{"title":"Approximately low-rank recovery from noisy and local measurements by convex program","authors":"Kiryung Lee, Rakshith Sharma Srinivasa, Marius Junge, Justin Romberg","doi":"10.1093/imaiai/iaad013","DOIUrl":"https://doi.org/10.1093/imaiai/iaad013","url":null,"abstract":"Abstract Low-rank matrix models have been universally useful for numerous applications, from classical system identification to more modern matrix completion in signal processing and statistics. The nuclear norm has been employed as a convex surrogate of the low-rankness since it induces a low-rank solution to inverse problems. While the nuclear norm for low rankness has an excellent analogy with the $ell _1$ norm for sparsity through the singular value decomposition, other matrix norms also induce low-rankness. Particularly as one interprets a matrix as a linear operator between Banach spaces, various tensor product norms generalize the role of the nuclear norm. We provide a tensor-norm-constrained estimator for the recovery of approximately low-rank matrices from local measurements corrupted with noise. A tensor-norm regularizer is designed to adapt to the local structure. We derive statistical analysis of the estimator over matrix completion and decentralized sketching by applying Maurey’s empirical method to tensor products of Banach spaces. The estimator provides a near-optimal error bound in a minimax sense and admits a polynomial-time algorithm for these applications.","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":"136085521","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

Universal consistency of Wasserstein k-NN classifier: a negative and some positive results Wasserstein k-NN分类器的普遍一致性:一个否定和一些肯定的结果

IF 1.6 4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad027

Donlapark Ponnoprat

引用次数: 0

Multivariate super-resolution without separation 无分离的多元超分辨率

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad024

Bakytzhan Kurmanbek, Elina Robeva

引用次数: 0

A manifold two-sample test study: integral probability metric with neural networks 流形双样本检验研究:基于神经网络的积分概率度量

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad018

Jie Wang, Minshuo Chen, Tuo Zhao, Wenjing Liao, Yao Xie

{"title":"A manifold two-sample test study: integral probability metric with neural networks","authors":"Jie Wang, Minshuo Chen, Tuo Zhao, Wenjing Liao, Yao Xie","doi":"10.1093/imaiai/iaad018","DOIUrl":"https://doi.org/10.1093/imaiai/iaad018","url":null,"abstract":"Abstract Two-sample tests are important areas aiming to determine whether two collections of observations follow the same distribution or not. We propose two-sample tests based on integral probability metric (IPM) for high-dimensional samples supported on a low-dimensional manifold. We characterize the properties of proposed tests with respect to the number of samples $n$ and the structure of the manifold with intrinsic dimension $d$. When an atlas is given, we propose a two-step test to identify the difference between general distributions, which achieves the type-II risk in the order of $n^{-1/max {d,2}}$. When an atlas is not given, we propose Hölder IPM test that applies for data distributions with $(s,beta )$-Hölder densities, which achieves the type-II risk in the order of $n^{-(s+beta )/d}$. To mitigate the heavy computation burden of evaluating the Hölder IPM, we approximate the Hölder function class using neural networks. Based on the approximation theory of neural networks, we show that the neural network IPM test has the type-II risk in the order of $n^{-(s+beta )/d}$, which is in the same order of the type-II risk as the Hölder IPM test. Our proposed tests are adaptive to low-dimensional geometric structure because their performance crucially depends on the intrinsic dimension instead of the data dimension.","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":"136266917","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

Fast and provable tensor robust principal component analysis via scaled gradient descent 快速和可证明的张量鲁棒主成分分析通过缩放梯度下降

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaad019

Harry Dong, Tian Tong, Cong Ma, Yuejie Chi

{"title":"Fast and provable tensor robust principal component analysis via scaled gradient descent","authors":"Harry Dong, Tian Tong, Cong Ma, Yuejie Chi","doi":"10.1093/imaiai/iaad019","DOIUrl":"https://doi.org/10.1093/imaiai/iaad019","url":null,"abstract":"Abstract An increasing number of data science and machine learning problems rely on computation with tensors, which better capture the multi-way relationships and interactions of data than matrices. When tapping into this critical advantage, a key challenge is to develop computationally efficient and provably correct algorithms for extracting useful information from tensor data that are simultaneously robust to corruptions and ill-conditioning. This paper tackles tensor robust principal component analysis (RPCA), which aims to recover a low-rank tensor from its observations contaminated by sparse corruptions, under the Tucker decomposition. To minimize the computation and memory footprints, we propose to directly recover the low-dimensional tensor factors—starting from a tailored spectral initialization—via scaled gradient descent (ScaledGD), coupled with an iteration-varying thresholding operation to adaptively remove the impact of corruptions. Theoretically, we establish that the proposed algorithm converges linearly to the true low-rank tensor at a constant rate that is independent with its condition number, as long as the level of corruptions is not too large. Empirically, we demonstrate that the proposed algorithm achieves better and more scalable performance than state-of-the-art tensor RPCA algorithms through synthetic experiments and real-world applications.","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":"136267080","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

Lossy compression of general random variables 一般随机变量的有损压缩

4区数学

Information and Inference-A Journal of the Ima Pub Date : 2023-04-27 DOI: 10.1093/imaiai/iaac035

Erwin Riegler, Helmut Bölcskei, Günther Koliander

引用次数: 0