Related papers: Classification of high-dimensional data with spike…
Estimating a covariance matrix and its associated principal components is a fundamental problem in contemporary statistics. While optimal estimation procedures have been developed with well-understood properties, the increasing demand for…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
In this work we consider the problem of estimating a high-dimensional $p \times p$ covariance matrix $\Sigma$, given $n$ observations of confounded data with covariance $\Sigma + \Gamma \Gamma^T$, where $\Gamma$ is an unknown $p \times q$…
Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…
We study the parameter estimation problem for a varying index coefficient model in high dimensions. Unlike the most existing works that iteratively estimate the parameters and link functions, based on the generalized Stein's identity, we…
High-dimensional sparse matrix data frequently arise in various applications. A notable example is the weighted word-word co-occurrence count data, which summarizes the weighted frequency of word pairs appearing within the same context…
Estimating a sparse covariance matrix is a fundamental problem in high-dimensional statistics. However, thresholding methods developed for independent data are generally not directly applicable to high-dimensional time series, where…
We consider high-dimensional measurement errors with high-frequency data. Our objective is on recovering the high-dimensional cross-sectional covariance matrix of the random errors with optimality. In this problem, not all components of the…
We propose a compressive classification framework for settings where the data dimensionality is significantly higher than the sample size. The proposed method, referred to as compressive regularized discriminant analysis (CRDA) is based on…
Given i.i.d. observations of a random vector $X \in \mathbb{R}^p$, we study the problem of estimating both its covariance matrix $\Sigma^*$, and its inverse covariance or concentration matrix {$\Theta^* = (\Sigma^*)^{-1}$.} We estimate…
We propose a modification of linear discriminant analysis, referred to as compressive regularized discriminant analysis (CRDA), for analysis of high-dimensional datasets. CRDA is specially designed for feature elimination purpose and can be…
We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…
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…
Sparse Principal Component Analysis (PCA) is a dimensionality reduction technique wherein one seeks a low-rank representation of a data matrix with additional sparsity constraints on the obtained representation. We consider two…
Using a low-dimensional parametrization of signals is a generic and powerful way to enhance performance in signal processing and statistical inference. A very popular and widely explored type of dimensionality reduction is sparsity; another…
The most effective dimensionality reduction procedures produce interpretable features from the raw input space while also providing good performance for downstream supervised learning tasks. For many methods, this requires optimizing one or…
This paper introduces a novel framework for dynamic classification in high dimensional spaces, addressing the evolving nature of class distributions over time or other index variables. Traditional discriminant analysis techniques are…
Dimensionality reduction is an important operation in information visualization, feature extraction, clustering, regression, and classification, especially for processing noisy high dimensional data. However, most existing approaches…
Many real-world datasets contain hidden structure that cannot be detected by simple linear correlations between input features. For example, latent factors may influence the data in a coordinated way, even though their effect is invisible…
Consider a two-class classification problem where we observe samples $(X_i, Y_i)$ for i = 1, ..., n, $X_i \in R^p$ and $Y_i$ in {0, 1}. Given $Y_i = k$, $X_i$ is assumed to follow a multivariate normal distribution with mean $\mu_k \in R^k$…