Related papers: Sparse Matrix Inversion with Scaled Lasso
Graphical Lasso (GL) is a popular method for learning the structure of an undirected graphical model, which is based on an $l_1$ regularization technique. The objective of this paper is to compare the computationally-heavy GL technique with…
For statistical modeling wherein the data regime is unfavorable in terms of dimensionality relative to the sample size, finding hidden sparsity in the ground truth can be critical in formulating an accurate statistical model. The so-called…
Estimating covariance matrices with high-dimensional complex data presents significant challenges, particularly concerning positive definiteness, sparsity, and numerical stability. Existing robust sparse estimators often fail to guarantee…
The purpose of model selection algorithms such as All Subsets, Forward Selection and Backward Elimination is to choose a linear model on the basis of the same set of data to which the model will be applied. Typically we have available a…
We improve upon the two-stage sparse vector autoregression (sVAR) method in Davis et al. (2016) by proposing an alternative two-stage modified sVAR method which relies on time series graphical lasso to estimate sparse inverse spectral…
This paper addresses the problem of identifying sparse linear time-invariant (LTI) systems from a single sample trajectory generated by the system dynamics. We introduce a Lasso-like estimator for the parameters of the system, taking into…
In this paper, we introduce Adaptive Cluster Lasso(ACL) method for variable selection in high dimensional sparse regression models with strongly correlated variables. To handle correlated variables, the concept of clustering or grouping…
We propose a simple and efficient algorithm for learning sparse invariant representations from unlabeled data with fast inference. When trained on short movies sequences, the learned features are selective to a range of orientations and…
In high-dimensional data analysis, regularization methods pursuing sparsity and/or low rank have received a lot of attention recently. To provide a proper amount of shrinkage, it is typical to use a grid search and a model comparison…
Standard likelihood penalties to learn Gaussian graphical models are based on regularising the off-diagonal entries of the precision matrix. Such methods, and their Bayesian counterparts, are not invariant to scalar multiplication of the…
Recovering latent structure from count data has received considerable attention in network inference, particularly when one seeks both cross-group interactions and within-group similarity patterns in bipartite networks, which is widely used…
An efficient nonlinear contrast source inversion scheme for electromagnetic imaging of sparse two-dimensional investigation domains is proposed. To avoid generating a sequence of linear sparse optimization problems, the non-linearity is…
In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with…
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 proposed a new penalized method in this paper to solve sparse Poisson Regression problems. Being different from $\ell_1$ penalized log-likelihood estimation, our new method can be viewed as penalized weighted score function method. We…
Sparse inverse covariance selection is a fundamental problem for analyzing dependencies in high dimensional data. However, such a problem is difficult to solve since it is NP-hard. Existing solutions are primarily based on convex…
We propose a Bayesian methodology for estimating spiked covariance matrices with jointly sparse structure in high dimensions. The spiked covariance matrix is reparametrized in terms of the latent factor model, where the loading matrix is…
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 propose a new method for supervised learning, especially suited to wide data where the number of features is much greater than the number of observations. The method combines the lasso ($\ell_1$) sparsity penalty with a quadratic penalty…
Sparse linear regression with ill-conditioned Gaussian random designs is widely believed to exhibit a statistical/computational gap, but there is surprisingly little formal evidence for this belief, even in the form of examples that are…