Journal of Multivariate Analysis最新文献

{"title":"Fisher’s pioneering work on discriminant analysis and its impact on Artificial Intelligence","authors":"Kanti V. Mardia","doi":"10.1016/j.jmva.2024.105341","DOIUrl":"10.1016/j.jmva.2024.105341","url":null,"abstract":"<div><p>Sir Ronald Aylmer Fisher opened many new areas in Multivariate Analysis, and the one which we will consider is discriminant analysis. Several papers by Fisher and others followed from his seminal paper in 1936 where he coined the name discrimination function. Historically, his four papers on discriminant analysis during 1936–1940 connect to the contemporaneous pioneering work of Hotelling and Mahalanobis. We revisit the famous iris data which Fisher used in his 1936 paper and in particular, test the hypothesis of multivariate normality for the data which he assumed. Fisher constructed his genetic discriminant motivated by this application and we provide a deeper insight into this construction; however, this construction has not been well understood as far as we know. We also indicate how the subject has developed along with the computer revolution, noting newer methods to carry out discriminant analysis, such as kernel classifiers, classification trees, support vector machines, neural networks, and deep learning. Overall, with computational power, the whole subject of Multivariate Analysis has changed its emphasis but the impact of this Fisher’s pioneering work continues as an integral part of supervised learning in Artificial Intelligence (AI).</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105341"},"PeriodicalIF":1.6,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141403667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Max-convolution processes with random shape indicator kernels","authors":"Pavel Krupskii ,&nbsp;Raphaël Huser","doi":"10.1016/j.jmva.2024.105340","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105340","url":null,"abstract":"<div><p>In this paper, we introduce a new class of models for spatial data obtained from max-convolution processes based on indicator kernels with random shape. We show that these models have appealing dependence properties including tail dependence at short distances and independence at long distances. We further consider max-convolutions between such processes and processes with tail independence, in order to separately control the bulk and tail dependence behaviors, and to increase flexibility of the model at longer distances, in particular, to capture intermediate tail dependence. We show how parameters can be estimated using a weighted pairwise likelihood approach, and we conduct an extensive simulation study to show that the proposed inference approach is feasible in relatively high dimensions and it yields accurate parameter estimates in most cases. We apply the proposed methodology to analyze daily temperature maxima measured at 100 monitoring stations in the state of Oklahoma, US. Our results indicate that our proposed model provides a good fit to the data, and that it captures both the bulk and the tail dependence structures accurately.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105340"},"PeriodicalIF":1.6,"publicationDate":"2024-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000472/pdfft?md5=6e148f4b405bc0c38b2fef0ced10dc6b&pid=1-s2.0-S0047259X24000472-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141313857","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Low-rank tensor regression for selection of grouped variables","authors":"Yang Chen,&nbsp;Ziyan Luo,&nbsp;Lingchen Kong","doi":"10.1016/j.jmva.2024.105339","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105339","url":null,"abstract":"<div><p>Low-rank tensor regression (LRTR) problems are widely studied in statistics and machine learning, in which the regressors are generally grouped by clustering strongly correlated variables or variables corresponding to different levels of the same predictive factor in many practical applications. By virtue of the idea of group selection in the classical linear regression framework, we propose an LRTR method for adaptive selection of grouped variables in this article, which is formulated as a group SLOPE penalized low-rank, orthogonally decomposable tensor optimization problem. Moreover, we introduce the notion of tensor group false discovery rate (TgFDR) to measure the group selection performance. The proposed regression method provably controls TgFDR and achieves the asymptotically minimax estimate under the assumption that variable groups are orthogonal to each other. Finally, an alternating minimization algorithm is developed for efficient problem resolution. We demonstrate the performance of our proposed method in group selection and low-rank estimation through simulation studies and real dataset analysis.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105339"},"PeriodicalIF":1.6,"publicationDate":"2024-06-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141323989","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Bias correction for kernel density estimation with spherical data","authors":"Yasuhito Tsuruta","doi":"10.1016/j.jmva.2024.105338","DOIUrl":"10.1016/j.jmva.2024.105338","url":null,"abstract":"<div><p>Kernel density estimations with spherical data can flexibly estimate the shape of an underlying density, including rotationally symmetric, skewed, and multimodal distributions. Standard estimators are generally based on rotationally symmetric kernel functions such as the von Mises kernel function. Unfortunately, their mean integrated squared error does not have root-<span><math><mi>n</mi></math></span> consistency and increasing the dimension slows its convergence rate. Therefore, this study aims to improve its accuracy by correcting this bias. It proposes bias correction methods by applying the generalized jackknifing method that can be generated from the von Mises kernel function. We also obtain the asymptotic mean integrated squared errors of the proposed estimators. We find that the convergence rates of the proposed estimators are higher than those of previous estimators. Further, a numerical experiment shows that the proposed estimators perform better than the von Mises kernel density estimators in finite samples in scenarios that are mixtures of von Mises densities.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105338"},"PeriodicalIF":1.6,"publicationDate":"2024-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141281345","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive directional estimator of the density in Rd for independent and mixing sequences","authors":"Sinda Ammous ,&nbsp;Jérôme Dedecker ,&nbsp;Céline Duval","doi":"10.1016/j.jmva.2024.105332","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105332","url":null,"abstract":"<div><p>A new multivariate density estimator for stationary sequences is obtained by Fourier inversion of the thresholded empirical characteristic function. This estimator does not depend on the choice of parameters related to the smoothness of the density; it is directly adaptive. We establish oracle inequalities valid for independent, <span><math><mi>α</mi></math></span>-mixing and <span><math><mi>τ</mi></math></span>-mixing sequences, which allows us to derive optimal convergence rates, up to a logarithmic loss. On general anisotropic Sobolev classes, the estimator adapts to the regularity of the unknown density but also achieves directional adaptivity. More precisely, the estimator is able to reach the convergence rate induced by the <em>best</em> Sobolev regularity of the density of <span><math><mrow><mi>A</mi><mi>X</mi></mrow></math></span>, where <span><math><mi>A</mi></math></span> belongs to a class of invertible matrices describing all the possible directions. The estimator is easy to implement and numerically efficient. It depends on the calibration of a parameter for which we propose an innovative numerical selection procedure, using the Euler characteristic of the thresholded areas.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105332"},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141290044","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Ordinal pattern dependence and multivariate measures of dependence","authors":"Angelika Silbernagel,&nbsp;Alexander Schnurr","doi":"10.1016/j.jmva.2024.105337","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105337","url":null,"abstract":"<div><p>Ordinal pattern dependence has been introduced in order to capture co-monotonic behavior between two time series. This concept has several features one would intuitively demand from a dependence measure. It was believed that ordinal pattern dependence satisfies the axioms which Grothe et al. (2014) proclaimed for a multivariate measure of dependence. In the present article we show that this is not true and that there is a mistake in the article by Betken et al. (2021). Furthermore, we show that ordinal pattern dependence satisfies a slightly modified set of axioms.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105337"},"PeriodicalIF":1.6,"publicationDate":"2024-05-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000447/pdfft?md5=1cb9743828786dd1e4dbfb081a6f213d&pid=1-s2.0-S0047259X24000447-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141323996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Parametric dependence between random vectors via copula-based divergence measures","authors":"Steven De Keyser,&nbsp;Irène Gijbels","doi":"10.1016/j.jmva.2024.105336","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105336","url":null,"abstract":"<div><p>This article proposes copula-based dependence quantification between multiple groups of random variables of possibly different sizes via the family of <span><math><mi>Φ</mi></math></span>-divergences. An axiomatic framework for this purpose is provided, after which we focus on the absolutely continuous setting assuming copula densities exist. We consider parametric and semi-parametric frameworks, discuss estimation procedures, and report on asymptotic properties of the proposed estimators. In particular, we first concentrate on a Gaussian copula approach yielding explicit and attractive dependence coefficients for specific choices of <span><math><mi>Φ</mi></math></span>, which are more amenable for estimation. Next, general parametric copula families are considered, with special attention to nested Archimedean copulas, being a natural choice for dependence modelling of random vectors. The results are illustrated by means of examples. Simulations and a real-world application on financial data are provided as well.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105336"},"PeriodicalIF":1.6,"publicationDate":"2024-05-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141239837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Tensor recovery in high-dimensional Ising models","authors":"Tianyu Liu ,&nbsp;Somabha Mukherjee ,&nbsp;Rahul Biswas","doi":"10.1016/j.jmva.2024.105335","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105335","url":null,"abstract":"<div><p>The <span><math><mi>k</mi></math></span>-tensor Ising model is a multivariate exponential family on a <span><math><mi>p</mi></math></span>-dimensional binary hypercube for modeling dependent binary data, where the sufficient statistic consists of all <span><math><mi>k</mi></math></span>-fold products of the observations, and the parameter is an unknown <span><math><mi>k</mi></math></span>-fold tensor, designed to capture higher-order interactions between the binary variables. In this paper, we describe an approach based on a penalization technique that helps us recover the signed support of the tensor parameter with high probability, assuming that no entry of the true tensor is too close to zero. The method is based on an <span><math><msub><mrow><mi>ℓ</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-regularized node-wise logistic regression, that recovers the signed neighborhood of each node with high probability. Our analysis is carried out in the high-dimensional regime, that allows the dimension <span><math><mi>p</mi></math></span> of the Ising model, as well as the interaction factor <span><math><mi>k</mi></math></span> to potentially grow to <span><math><mi>∞</mi></math></span> with the sample size <span><math><mi>n</mi></math></span>. We show that if the minimum interaction strength is not too small, then consistent recovery of the entire signed support is possible if one takes <span><math><mrow><mi>n</mi><mo>=</mo><mi>Ω</mi><mrow><mo>(</mo><msup><mrow><mrow><mo>(</mo><mi>k</mi><mo>!</mo><mo>)</mo></mrow></mrow><mrow><mn>8</mn></mrow></msup><msup><mrow><mi>d</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>log</mo><mfenced><mrow><mfrac><mrow><mi>p</mi><mo>−</mo><mn>1</mn></mrow><mrow><mi>k</mi><mo>−</mo><mn>1</mn></mrow></mfrac></mrow></mfenced><mo>)</mo></mrow></mrow></math></span> samples, where <span><math><mi>d</mi></math></span> denotes the maximum degree of the hypernetwork in question. Our results are validated in two simulation settings, and applied on a real neurobiological dataset consisting of multi-array electro-physiological recordings from the mouse visual cortex, to model higher-order interactions between the brain regions.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105335"},"PeriodicalIF":1.6,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141164340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Distribution-on-distribution regression with Wasserstein metric: Multivariate Gaussian case","authors":"Ryo Okano ,&nbsp;Masaaki Imaizumi","doi":"10.1016/j.jmva.2024.105334","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105334","url":null,"abstract":"<div><p>Distribution data refer to a data set in which each sample is represented as a probability distribution, a subject area that has received increasing interest in the field of statistics. Although several studies have developed distribution-to-distribution regression models for univariate variables, the multivariate scenario remains under-explored due to technical complexities. In this study, we introduce models for regression from one Gaussian distribution to another, using the Wasserstein metric. These models are constructed using the geometry of the Wasserstein space, which enables the transformation of Gaussian distributions into components of a linear matrix space. Owing to their linear regression frameworks, our models are intuitively understandable, and their implementation is simplified because of the optimal transport problem’s analytical solution between Gaussian distributions. We also explore a generalization of our models to encompass non-Gaussian scenarios. We establish the convergence rates of in-sample prediction errors for the empirical risk minimizations in our models. In comparative simulation experiments, our models demonstrate superior performance over a simpler alternative method that transforms Gaussian distributions into matrices. We present an application of our methodology using weather data for illustration purposes.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105334"},"PeriodicalIF":1.6,"publicationDate":"2024-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0047259X24000411/pdfft?md5=dea43975f3758fd74adfc88e822be366&pid=1-s2.0-S0047259X24000411-main.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141239836","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Sparse subspace clustering in diverse multiplex network model","authors":"Majid Noroozi ,&nbsp;Marianna Pensky","doi":"10.1016/j.jmva.2024.105333","DOIUrl":"https://doi.org/10.1016/j.jmva.2024.105333","url":null,"abstract":"<div><p>The paper considers the DIverse MultiPLEx (DIMPLE) network model, where all layers of the network have the same collection of nodes and are equipped with the Stochastic Block Models. In addition, all layers can be partitioned into groups with the same community structures, although the layers in the same group may have different matrices of block connection probabilities. To the best of our knowledge, the DIMPLE model, introduced in Pensky and Wang (2021), presents the most broad SBM-equipped binary multilayer network model on the same set of nodes and, thus, generalizes a multitude of papers that study more restrictive settings. Under the DIMPLE model, the main task is to identify the groups of layers with the same community structures since the matrices of block connection probabilities act as nuisance parameters under the DIMPLE paradigm. The main contribution of the paper is achieving the strongly consistent between-layer clustering by using Sparse Subspace Clustering (SSC), the well-developed technique in computer vision. In addition, SSC allows to handle much larger networks than spectral clustering, and is perfectly suitable for application of parallel computing. Moreover, our paper is the first one to obtain precision guarantees for SSC when it is applied to binary data.</p></div>","PeriodicalId":16431,"journal":{"name":"Journal of Multivariate Analysis","volume":"203 ","pages":"Article 105333"},"PeriodicalIF":1.6,"publicationDate":"2024-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141095842","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}