Related papers: Phase Transitions in Sparse PCA
Sparse PCA is the optimization problem obtained from PCA by adding a sparsity constraint on the principal components. Sparse PCA is NP-hard and hard to approximate even in the single-component case. In this paper we settle the computational…
Approximate message passing (AMP) has emerged both as a popular class of iterative algorithms and as a powerful analytic tool in a wide range of statistical estimation problems and statistical physics models. A well established line of AMP…
Sparse Principal Component Analysis (sPCA) is a popular matrix factorization approach based on Principal Component Analysis (PCA) that combines variance maximization and sparsity with the ultimate goal of improving data interpretation. When…
Conformal prediction has emerged as a powerful tool for building prediction intervals that are valid in a distribution-free way. However, its evaluation may be computationally costly, especially in the high-dimensional setting where the…
Sparse principal component analysis (sparse PCA) aims at finding a sparse basis to improve the interpretability over the dense basis of PCA, meanwhile the sparse basis should cover the data subspace as much as possible. In contrast to most…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
Approximate Message Passing (AMP) algorithms enable precise characterization of certain classes of random objects in the high-dimensional limit, and have found widespread applications in fields such as signal processing, statistics, and…
Sparse principal component analysis (sparse PCA) is a widely used technique for dimensionality reduction in multivariate analysis, addressing two key limitations of standard PCA. First, sparse PCA can be implemented in high-dimensional low…
Vector approximate message passing (VAMP) is an efficient approximate inference algorithm used for generalized linear models. Although VAMP exhibits excellent performance, particularly when measurement matrices are sampled from rotationally…
In statistical learning for real-world large-scale data problems, one must often resort to "streaming" algorithms which operate sequentially on small batches of data. In this work, we present an analysis of the information-theoretic limits…
We consider the following multi-component sparse PCA problem: given a set of data points, we seek to extract a small number of sparse components with disjoint supports that jointly capture the maximum possible variance. These components can…
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…
We establish minimax optimal rates of convergence for estimation in a high dimensional additive model assuming that it is approximately sparse. Our results reveal an interesting phase transition behavior universal to this class of high…
The generalized approximate message passing (GAMP) algorithm under the Bayesian setting shows advantage in recovering under-sampled sparse signals from corrupted observations. Compared to conventional convex optimization methods, it has a…
We investigate a generalized framework to estimate a latent low-rank plus sparse tensor, where the low-rank tensor often captures the multi-way principal components and the sparse tensor accounts for potential model mis-specifications or…
Principal component analysis (PCA) has been a prominent tool for high-dimensional data analysis. Online algorithms that estimate the principal component by processing streaming data are of tremendous practical and theoretical interests.…
We consider the problem of estimating a signal from measurements obtained via a generalized linear model. We focus on estimators based on approximate message passing (AMP), a family of iterative algorithms with many appealing features: the…
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…
We consider dictionary learning and blind calibration for signals and matrices created from a random ensemble. We study the mean-squared error in the limit of large signal dimension using the replica method and unveil the appearance of…
This paper proposes sparse and easy-to-interpret proximate factors to approximate statistical latent factors. Latent factors in a large-dimensional factor model can be estimated by principal component analysis (PCA), but are usually hard to…