Related papers: Signal extraction approach for sparse multivariate…
This paper proposes an innovative method for constructing confidence intervals and assessing p-values in statistical inference for high-dimensional linear models. The proposed method has successfully broken the high-dimensional inference…
The interdependence and high dimensionality of multivariate signals present significant challenges for denoising, as conventional univariate methods often struggle to capture the complex interactions between variables. A successful approach…
Consider the regression problem where the response $Y\in\mathbb{R}$ and the covariate $X\in\mathbb{R}^d$ for $d\geq 1$ are \textit{unmatched}. Under this scenario, we do not have access to pairs of observations from the distribution of $(X,…
Recently there has been many works on adaptive subspace filtering in the signal processing literature. Most of them are concerned with tracking the signal subspace spanned by the eigenvectors corresponding to the eigenvalues of the…
In this paper we propose a computationally efficient algorithm for on-line variable selection in multivariate regression problems involving high dimensional data streams. The algorithm recursively extracts all the latent factors of a…
Suppose we are given a matrix that is formed by adding an unknown sparse matrix to an unknown low-rank matrix. Our goal is to decompose the given matrix into its sparse and low-rank components. Such a problem arises in a number of…
In this paper, we propose to decompose the canonical parameter of a multinomial model into a set of participant scores and category scores. External information about the participants or the categories can be used to restrict these scores.…
Low-rank decomposition has emerged as a vital tool for enhancing parameter efficiency in neural network architectures, gaining traction across diverse applications in machine learning. These techniques significantly lower the number of…
Our research proposes a novel method for reducing the dimensionality of functional data, specifically for the case where the response is a scalar and the predictor is a random function. Our method utilizes distance covariance, and has…
We consider a high-dimensional linear regression problem. Unlike many papers on the topic, we do not require sparsity of the regression coefficients; instead, our main structural assumption is a decay of eigenvalues of the covariance matrix…
This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least…
Dimensionality reduction is an effective method for learning high-dimensional data, which can provide better understanding of decision boundaries in human-readable low-dimensional subspace. Linear methods, such as principal component…
Canonical Correlation Analysis (CCA) is a widespread technique for discovering linear relationships between two sets of variables $X \in \mathbb{R}^{n \times p}$ and $Y \in \mathbb{R}^{n \times q}$. In high dimensions however, standard…
This paper develops an approach to inference in a linear regression model when the number of potential explanatory variables is larger than the sample size. The approach treats each regression coefficient in turn as the interest parameter,…
The root-cause diagnostics of product quality defects in multistage manufacturing processes often requires a joint identification of crucial stages and process variables. To meet this requirement, this paper proposes a novel penalized…
Sparse support recovery arises in many applications in communications and signal processing. Existing methods tackle sparse support recovery problems for a given measurement matrix, and cannot flexibly exploit the properties of sparsity…
Homogeneity, low rank, and sparsity are three widely adopted assumptions in multi-response regression models to address the curse of dimensionality and improve estimation accuracy. However, there is limited literature that examines these…
Sparse covariance matrices play crucial roles by encoding the interdependencies between variables in numerous fields such as genetics and neuroscience. Despite substantial studies on sparse covariance matrices, existing methods face several…
In many practical applications such as direction-of-arrival (DOA) estimation and line spectral estimation, the sparsifying dictionary is usually characterized by a set of unknown parameters in a continuous domain. To apply the conventional…
We develop a new method to fit the multivariate response linear regression model that exploits a parametric link between the regression coefficient matrix and the error covariance matrix. Specifically, we assume that the correlations…