Related papers: Efficient Canonical Correlation Analysis with Spar…
Sparse Principal Component Analysis (Sparse PCA) is a pivotal tool in data analysis and dimensionality reduction. However, Sparse PCA is a challenging problem in both theory and practice: it is known to be NP-hard and current exact methods…
This article critically assesses the utility of the classical statistical technique of Canonical Correlation Analysis (CCA) for studying spatial associations and proposes a new approach to enhance it. Unlike bivariate correlation analysis,…
Sparse principal component analysis (SPCA) is widely used for dimensionality reduction and feature extraction in high-dimensional data analysis. Despite many methodological and theoretical developments in the past two decades, the…
Bayesian variable selection methods are powerful techniques for fitting and inferring on sparse high-dimensional linear regression models. However, many are computationally intensive or require restrictive prior distributions on model…
Canonical correlation analysis (CCA) is a popular technique for learning representations that are maximally correlated across multiple views in data. In this paper, we extend the CCA based framework for learning a multiview mixture model.…
In this paper, we study high-dimensional sparse Quadratic Discriminant Analysis (QDA) and aim to establish the optimal convergence rates for the classification error. Minimax lower bounds are established to demonstrate the necessity of…
I introduce Forecastable Component Analysis (ForeCA), a novel dimension reduction technique for temporally dependent signals. Based on a new forecastability measure, ForeCA finds an optimal transformation to separate a multivariate time…
Sparsity is a fundamental modeling principle in statistics, signal processing, and data science. However, optimization with sparsity constraints is notoriously difficult. We introduce a new convex relaxation framework for {sparse…
Sparse principal component analysis (PCA) is an important technique for dimensionality reduction of high-dimensional data. However, most existing sparse PCA algorithms are based on non-convex optimization, which provide little guarantee on…
Sparse Principal Component Analysis (SPCA) is an important technique for high-dimensional data analysis, improving interpretability by imposing sparsity on principal components. However, existing methods often fail to simultaneously…
Multi-block CCA constructs linear relationships explaining coherent variations across multiple blocks of data. We view the multi-block CCA problem as finding leading generalized eigenvectors and propose to solve it via a proximal gradient…
Canonical correlation analysis (CCA) is a valuable method for interpreting cross-covariance across related datasets of different dimensionality. There are many potential applications of CCA to neuroimaging data analysis. For instance, CCA…
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…
Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…
We present deep variational canonical correlation analysis (VCCA), a deep multi-view learning model that extends the latent variable model interpretation of linear CCA to nonlinear observation models parameterized by deep neural networks.…
In this paper we initiate the study of whether or not sparse estimation tasks can be performed efficiently in high dimensions, in the robust setting where an $\eps$-fraction of samples are corrupted adversarially. We study the natural…
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…
The sum-of-correlations (SUMCOR) formulation of generalized canonical correlation analysis (GCCA) seeks highly correlated low-dimensional representations of different views via maximizing pairwise latent similarity of the views. SUMCOR is…
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…
Canonical correlation analysis (CCA) is a state-of-the-art method for frequency recognition in steady-state visual evoked potential (SSVEP)-based brain-computer interface (BCI) systems. Various extended methods have been developed, and…