Related papers: Fast and Adaptive Sparse Precision Matrix Estimati…
To accelerate deep CNN models, this paper proposes a novel spatially adaptive framework that can dynamically generate pixel-wise sparsity according to the input image. The sparse scheme is pixel-wise refined, regional adaptive under a…
This paper is concerned with the problem of approximating the determinant of A for a large sparse symmetric positive definite matrix A. It is shown that an efficient solution of this problem is obtained by using a sparse approximate inverse…
In several applications, the underlying structure of the data allows for the samples to be organized into a matrix variate form. In such settings, the underlying row and column covariance matrices are fundamental quantities of interest. We…
We present a novel binary convex reformulation of the sparse regression problem that constitutes a new duality perspective. We devise a new cutting plane method and provide evidence that it can solve to provable optimality the sparse…
We present a method for estimating sparse high-dimensional inverse covariance and partial correlation matrices, which exploits the connection between the inverse covariance matrix and linear regression. The method is a two-stage estimation…
The computational cost of many signal processing and machine learning techniques is often dominated by the cost of applying certain linear operators to high-dimensional vectors. This paper introduces an algorithm aimed at reducing the…
In this work we construct an optimal shrinkage estimator for the precision matrix in high dimensions. We consider the general asymptotics when the number of variables $p\rightarrow\infty$ and the sample size $n\rightarrow\infty$ so that…
We propose a new method of learning a sparse nonnegative-definite target matrix. Our primary example of the target matrix is the inverse of a population covariance or correlation matrix. The algorithm first estimates each column of the…
The computational complexity of simultaneous inference methods in high-dimensional linear regression models quickly increases with the number variables. This paper proposes a computationally efficient method based on the Moore-Penrose…
The need for fast sparse optimization is emerging, e.g., to deal with large-dimensional data-driven problems and to track time-varying systems. In the framework of linear sparse optimization, the iterative shrinkage-thresholding algorithm…
We study the problem of estimating from data, a sparse approximation to the inverse covariance matrix. Estimating a sparsity constrained inverse covariance matrix is a key component in Gaussian graphical model learning, but one that is…
We apply a method recently introduced to the statistical literature to directly estimate the precision matrix from an ensemble of samples drawn from a corresponding Gaussian distribution. Motivated by the observation that cosmological…
Sparse Inverse Covariance Estimation (SICE) is useful in many practical data analyses. Recovering the connectivity, non-connectivity graph of covariates is classified amongst the most important data mining and learning problems. In this…
Matrix completion constantly receives tremendous attention from many research fields. It is commonly applied for recommender systems such as movie ratings, computer vision such as image reconstruction or completion, multi-task learning such…
We propose novel randomized optimization methods for high-dimensional convex problems based on restrictions of variables to random subspaces. We consider oblivious and data-adaptive subspaces and study their approximation properties via…
We study the problem of estimating precision matrices in Gaussian distributions that are multivariate totally positive of order two ($\mathrm{MTP}_2$). The precision matrix in such a distribution is an M-matrix. This problem can be…
We address the subset selection problem for matrices, where the goal is to select a subset of $k$ columns from a "short-and-fat" matrix $X \in \mathbb{R}^{m \times n}$, such that the pseudoinverse of the sampled submatrix has as small…
A precision matrix is the inverse of a covariance matrix. In this paper, we study the problem of estimating the precision matrix with a known graphical structure under high-dimensional settings. We propose a simple estimator of the…
Computation of the large sparse matrix exponential has been an important topic in many fields, such as network and finite-element analysis. The existing scaling and squaring algorithm (SSA) is not suitable for the computation of the large…
Recently, a class of algorithms combining classical fixed point iterations with repeated random sparsification of approximate solution vectors has been successfully applied to eigenproblems with matrices as large as $10^{108} \times…