相关论文: Sparsistency and agnostic inference in sparse PCA

A fundamental concept in control theory is that of controllability, where any system state can be reached through an appropriate choice of control inputs. Indeed, a large body of classical and modern approaches are designed for controllable…

Sparse methods are the standard approach to obtain interpretable models with high prediction accuracy. Alternatively, algorithmic ensemble methods can achieve higher prediction accuracy at the cost of loss of interpretability. However, the…

Singular value decomposition (SVD) based principal component analysis (PCA) breaks down in the high-dimensional and limited sample size regime below a certain critical eigen-SNR that depends on the dimensionality of the system and the…

Sparse principal component analysis (PCA) is a well-established dimensionality reduction technique that is often used for unsupervised feature selection (UFS). However, determining the regularization parameters is rather challenging, and…

Confidence sets based on sparse estimators are shown to be large compared to more standard confidence sets, demonstrating that sparsity of an estimator comes at a substantial price in terms of the quality of the estimator. The results are…

In this paper, we provide a general methodology to draw statistical inferences on individual signal coordinates or linear combinations of them in sparse phase retrieval. Given an initial estimator for the targeting parameter (some simple…

Principal Component Analysis (PCA) has been used to study the pathogenesis of diseases. To enhance the interpretability of classical PCA, various improved PCA methods have been proposed to date. Among these, a typical method is the…

We consider the problem of maximizing the variance explained from a data matrix using orthogonal sparse principal components that have a support of fixed cardinality. While most existing methods focus on building principal components (PCs)…

Regularized variants of Principal Components Analysis, especially Sparse PCA and Functional PCA, are among the most useful tools for the analysis of complex high-dimensional data. Many examples of massive data, have both sparse and…

Sparse principal component analysis (sPCA) has become one of the most widely used techniques for dimensionality reduction in high-dimensional datasets. The main challenge underlying sPCA is to estimate the first vector of loadings of the…

Given a sample covariance matrix, we examine the problem of maximizing the variance explained by a linear combination of the input variables while constraining the number of nonzero coefficients in this combination. This is known as sparse…

Randomized algorithms can be used to speed up the analysis of large datasets. In this paper, we develop a unified methodology for statistical inference via randomized sketching or projections in two of the most fundamental problems in…

Sparse Principal Component Analysis (sparse PCA) is a fundamental dimension-reduction tool that enhances interpretability in various high-dimensional settings. An important variant of sparse PCA studies the scenario when samples are…

Statistical sufficiency formalizes the notion of data reduction. In the decision theoretic interpretation, once a model is chosen all inferences should be based on a sufficient statistic. However, suppose we start with a set of procedures…

We propose methodology for estimation of sparse precision matrices and statistical inference for their low-dimensional parameters in a high-dimensional setting where the number of parameters $p$ can be much larger than the sample size. We…

For high-dimensional inference problems, statisticians have a number of competing interests. On the one hand, procedures should provide accurate estimation, reliable structure learning, and valid uncertainty quantification. On the other…

Sparse Principal Component Analysis (SPCA) and Sparse Linear Regression (SLR) have a wide range of applications and have attracted a tremendous amount of attention in the last two decades as canonical examples of statistical problems in…

This paper proposes a sparse regression method that continuously interpolates between Forward Stepwise selection (FS) and the LASSO. When tuned appropriately, our solutions are much sparser than typical LASSO fits but, unlike FS fits,…

We study high-dimensional sparse estimation tasks in a robust setting where a constant fraction of the dataset is adversarially corrupted. Specifically, we focus on the fundamental problems of robust sparse mean estimation and robust sparse…

The state-of-the-art automotive radars employ multidimensional discrete Fourier transforms (DFT) in order to estimate various target parameters. The DFT is implemented using the fast Fourier transform (FFT), at sample and computational…