Related papers: Structured Sparsity Promoting Functions
We study the problem of variable selection in convex nonparametric least squares (CNLS). Whereas the least absolute shrinkage and selection operator (Lasso) is a popular technique for least squares, its variable selection performance is…
The present work investigates the segmentation of textures by formulating it as a strongly convex optimization problem, aiming to favor piecewise constancy of fractal features (local variance and local regularity) widely used to model…
In the area of sparse recovery, numerous researches hint that non-convex penalties might induce better sparsity than convex ones, but up until now those corresponding non-convex algorithms lack convergence guarantees from the initial…
Submodular functions are relevant to machine learning for at least two reasons: (1) some problems may be expressed directly as the optimization of submodular functions and (2) the lovasz extension of submodular functions provides a useful…
In high-dimensions, many variable selection methods, such as the lasso, are often limited by excessive variability and rank deficiency of the sample covariance matrix. Covariance sparsity is a natural phenomenon in high-dimensional…
Functional principal component analysis (FPCA) is a fundamental tool and has attracted increasing attention in recent decades, while existing methods are restricted to data with a single or finite number of random functions (much smaller…
We study convex optimization problems where disjoint blocks of variables are controlled by binary indicator variables that are also subject to conditions, e.g., cardinality. Several classes of important examples can be formulated in such a…
This paper presents a novel framework for nonconvex enhancement of minimization induced (MI) penalties while preserving the overall convexity of associated regularization models. MI penalties enable the adaptation to certain signal…
This work studies the problem of sparse signal recovery with automatic grouping of variables. To this end, we investigate sorted nonsmooth penalties as a regularization approach for generalized linear models. We focus on a family of sorted…
Variable selection for models including interactions between explanatory variables often needs to obey certain hierarchical constraints. The weak or strong structural hierarchy requires that the existence of an interaction term implies at…
A key problem in statistics and machine learning is the determination of network structure from data. We consider the case where the structure of the graph to be reconstructed is known to be scale-free. We show that in such cases it is…
Under the linear regression framework, we study the variable selection problem when the underlying model is assumed to have a small number of nonzero coefficients (i.e., the underlying linear model is sparse). Non-convex penalties in…
We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…
Sparse covariates are frequent in classification and regression problems and in these settings the task of variable selection is usually of interest. As it is well known, sparse statistical models correspond to situations where there are…
Mixed-effect models are very popular for analyzing data with a hierarchical structure, e.g. repeated observations within subjects in a longitudinal design, patients nested within centers in a multicenter design. However, recently, due to…
In many scientific studies, it becomes increasingly important to delineate the causal pathways through a large number of mediators, such as genetic and brain mediators. Structural equation modeling (SEM) is a popular technique to estimate…
A simple sparse coding mechanism appears in the sensory systems of several organisms: to a coarse approximation, an input $x \in \R^d$ is mapped to much higher dimension $m \gg d$ by a random linear transformation, and is then sparsified by…
Inter-area oscillations in bulk power systems are typically poorly controllable by means of local decentralized control. Recent research efforts have been aimed at developing wide- area control strategies that involve communication of…
We introduce a novel Bayesian approach for both covariate selection and sparse precision matrix estimation in the context of high-dimensional Gaussian graphical models involving multiple responses. Our approach provides a sparse estimation…
We study the problem of detection of a high-dimensional signal function in the white Gaussian noise model. As well as a smoothness assumption on the signal function, we assume an additive sparse condition on the latter. The detection…