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多成分高斯混合模型下 EM 算法的收敛与最优性AI 解读

Summary Gaussian mixture models are fundamental statistical tools for modelling heterogeneous data. Due to the nonconcavity of the likelihood function, the expectation-maximization (EM) algorithm is widely used for parameter estimation of each Gaussian component. Existing analyses of the EM algorithm’s convergence to the true parameter focus on either the two-component case or multi-component settings with known mixing probabilities and isotropic covariance matrices. In this…

采用逐次提取 varimax 旋转的最优传统因子分析AI 解读

Vintage factor analysis is one important type of factor analysis that aims to first find a low-dimensional representation of the original data, and then to seek a rotation such that the rotated low-dimensional representation is scientifically meaningful. The most widely used vintage factor analysis is the Principal Component Analysis (PCA) followed by the varimax rotation. Despite its popularity, little theoretical guarantee can be provided to date mainly because varimax…

存在隐变量的高维多响应回归推断AI 解读

This article studies the inference of the regression coefficient matrix under multivariate response linear regressions in the presence of hidden variables. A novel procedure for constructing confidence intervals of entries of the coefficient matrix is proposed. Our method first uses the multivariate nature of the responses by estimating and adjusting the hidden effect to construct an initial estimator of the coefficient matrix. By further deploying a low-dimensional…

高维高斯潜在混合模型中的插值判别函数AI 解读

Abstract This paper considers binary classification of high-dimensional features under a postulated model with a low-dimensional latent Gaussian mixture structure and nonvanishing noise. A generalized least-squares estimator is used to estimate the direction of the optimal separating hyperplane. The estimated hyperplane is shown to interpolate on the training data. While the direction vector can be consistently estimated, as could be expected from recent results in linear…

高维潜在因子模型中的最优判别分析AI 解读

In high-dimensional classification problems, a commonly used approach is to first project the high-dimensional features into a lower-dimensional space, and base the classification on the resulting lower-dimensional projections. In this paper, we formulate a latent-variable model with a hidden low-dimensional structure to justify this two-step procedure and to guide which projection to choose. We propose a computationally efficient classifier that takes certain principal…

主题模型中稀疏主题分布的似然估计及 Wasserstein 文档距离应用AI 解读

This paper studies the estimation of high-dimensional, discrete, possibly sparse, mixture models in the context of topic models. The data consists of observed multinomial counts of p words across n independent documents. In topic models, the p×n expected word frequency matrix is assumed to be factorized as a p×K word-topic matrix A and a K×n topic-document matrix T. Since columns of both matrices represent conditional probabilities belonging to probability simplices, columns…

含隐变量的多响应回归自适应估计AI 解读

A prominent concern of scientific investigators is the presence of unobserved hidden variables in association analysis. Ignoring hidden variables often yields biased statistical results and misleading scientific conclusions. Motivated by this practical issue, this paper studies the multivariate response regression with hidden variables, Y=(Ψ∗)TX+(B∗)TZ+E, where Y∈Rm is the response vector, X∈Rp is the observable feature, Z∈RK represents the vector of unobserved hidden…

结构化因子模型的自适应估计及其在重叠聚类中的应用AI 解读

This work introduces a novel estimation method, called LOVE, of the entries and structure of a loading matrix $A$ in a latent factor model $X=AZ+E$, for an observable random vector $X\in \mathbb{R}^{p}$, with correlated unobservable factors $Z\in \mathbb{R}^{K}$, with $K$ unknown, and uncorrelated noise $E$. Each row of $A$ is scaled, and allowed to be sparse. In order to identify the loading matrix $A$, we require the existence of pure variables, which are components of $X$…

高维多响应回归中系数矩阵秩的自适应估计AI 解读

We consider the multivariate response regression problem with a regression coefficient matrix of low, unknown rank. In this setting, we analyze a new criterion for selecting the optimal reduced rank. This criterion differs notably from the one proposed in Bunea, She and Wegkamp (Ann. Statist. 39 (2011) 1282–1309) in that it does not require estimation of the unknown variance of the noise, nor does it depend on a delicate choice of a tuning parameter. We develop an iterative,…