Related papers: Sparse canonical correlation analysis from a predi…

The CUR decomposition provides an approximation of a matrix $X$ that has low reconstruction error and that is sparse in the sense that the resulting approximation lies in the span of only a few columns of $X$. In this regard, it appears to…

We explore estimation and forecast accuracy for sparse linear models, focusing on scenarios where both predictors and errors carry serial correlations. We establish a clear link between predictor serial correlation and the performance of…

We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small…

The topic of this tutorial is Least Squares Sparse Principal Components Analysis (LS SPCA) which is a simple method for computing approximated Principal Components which are combinations of only a few of the observed variables. Analogously…

We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…

We propose new methods for multivariate linear regression when the regression coefficient matrix is sparse and the error covariance matrix is dense. We assume that the error covariance matrix has equicorrelation across the response…

In this paper, we compared the general forms of CCA and PLS on three simulated and two empirical datasets, all having large sample sizes. We took successively smaller subsamples of these data to evaluate sensitivity, reliability, and…

Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…

Principal components analysis (PCA) is the optimal linear auto-encoder of data, and it is often used to construct features. Enforcing sparsity on the principal components can promote better generalization, while improving the…

Recent work has sought to understand the behavior of neural networks by comparing representations between layers and between different trained models. We examine methods for comparing neural network representations based on canonical…

In this paper, we study the problem of sparse Principal Component Analysis (PCA) in the high-dimensional setting with missing observations. Our goal is to estimate the first principal component when we only have access to partial…

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…

The locally competitive algorithm (LCA) can solve sparse coding problems across a wide range of use cases. Recently, convolution-based LCA approaches have been shown to be highly effective for enhancing robustness for image recognition…

Sparse modeling is a powerful framework for data analysis and processing. Traditionally, encoding in this framework is performed by solving an L1-regularized linear regression problem, commonly referred to as Lasso or Basis Pursuit. In this…

Sparse estimation for Gaussian graphical models is a crucial technique for making the relationships among numerous observed variables more interpretable and quantifiable. Various methods have been proposed, including graphical lasso, which…

Probabilistic principal component analysis (PPCA) seeks a low dimensional representation of a data set in the presence of independent spherical Gaussian noise, Sigma = (sigma^2)*I. The maximum likelihood solution for the model is an…

We examine the linear regression problem in a challenging high-dimensional setting with correlated predictors where the vector of coefficients can vary from sparse to dense. In this setting, we propose a combination of probabilistic…

This paper considers the problem of canonical-correlation analysis (CCA) (Hotelling, 1936) and, more broadly, the generalized eigenvector problem for a pair of symmetric matrices. These are two fundamental problems in data analysis and…

In this paper, we propose a mixture of probabilistic partial canonical correlation analysis (MPPCCA) that extracts the Causal Patterns from two multivariate time series. Causal patterns refer to the signal patterns within interactions of…

In this paper, we consider the Group Lasso estimator of the covariance matrix of a stochastic process corrupted by an additive noise. We propose to estimate the covariance matrix in a high-dimensional setting under the assumption that the…