Related papers: Regularized Estimation of Sparse Spectral Precisio…
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…
Simultaneous feature selection and non-linear function estimation is challenging in modeling, especially in high-dimensional settings where the number of variables exceeds the available sample size. In this article, we investigate the…
We consider the problem of learning a graph modeling the statistical relations of the $d$ variables from a dataset with $n$ samples $X \in \mathbb{R}^{n \times d}$. Standard approaches amount to searching for a precision matrix $\Theta$…
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…
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…
The goal of Sparse Convex Optimization is to optimize a convex function $f$ under a sparsity constraint $s\leq s^*\gamma$, where $s^*$ is the target number of non-zero entries in a feasible solution (sparsity) and $\gamma\geq 1$ is an…
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
High dimensional covariance estimation and graphical models is a contemporary topic in statistics and machine learning having widespread applications. An important line of research in this regard is to shrink the extreme spectrum of the…
We consider the problem of inferring the conditional independence graph (CIG) of a sparse, high-dimensional, stationary matrix-variate Gaussian time series. All past work on high-dimensional matrix graphical models assumes that independent…
Volterra and polynomial regression models play a major role in nonlinear system identification and inference tasks. Exciting applications ranging from neuroscience to genome-wide association analysis build on these models with the…
Sparse linear models are one of several core tools for interpretable machine learning, a field of emerging importance as predictive models permeate decision-making in many domains. Unfortunately, sparse linear models are far less flexible…
Precision matrix estimation is a cornerstone concept in statistics, economics, and finance. Despite advances in recent years, estimation methods that are simultaneously (i) dense, (ii) consistent, and (iii) model-free are lacking. While…
High-dimensional statistical learning (HDSL) has wide applications in data analysis, operations research, and decision-making. Despite the availability of multiple theoretical frameworks, most existing HDSL schemes stipulate the following…
In additive models with many nonparametric components, a number of regularized estimators have been proposed and proven to attain various error bounds under different combinations of sparsity and fixed smoothness conditions. Some of these…
In high-dimensional statistical inference in which the number of parameters to be estimated is larger than that of the holding data, regularized linear estimation techniques are widely used. These techniques have, however, some drawbacks.…
We consider the problem of parameter estimation in a high-dimensional generalized linear model. Spectral methods obtained via the principal eigenvector of a suitable data-dependent matrix provide a simple yet surprisingly effective…
How can we compute the pseudoinverse of a sparse feature matrix efficiently and accurately for solving optimization problems? A pseudoinverse is a generalization of a matrix inverse, which has been extensively utilized as a fundamental…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
Sparse recovery is one of the most fundamental and well-studied inverse problems. Standard statistical formulations of the problem are provably solved by general convex programming techniques and more practical, fast (nearly-linear time)…
For some special data in reality, such as the genetic data, adjacent genes may have the similar function. Thus ensuring the smoothness between adjacent genes is highly necessary. But, in this case, the standard lasso penalty just doesn't…