Related papers: Collaborative Hierarchical Sparse Modeling
In this paper, we propose a general collaborative sparse representation framework for multi-sensor classification, which takes into account the correlations as well as complementary information between heterogeneous sensors simultaneously…
We introduce the localized Lasso, which is suited for learning models that are both interpretable and have a high predictive power in problems with high dimensionality $d$ and small sample size $n$. More specifically, we consider a function…
The performance of machine learning and pattern recognition algorithms generally depends on data representation. That is why, much of the current effort in performing machine learning algorithms goes into the design of preprocessing…
Many classification approaches first represent a test sample using the training samples of all the classes. This collaborative representation is then used to label the test sample. It was a common belief that sparseness of the…
Sparse coding algorithm is an learning algorithm mainly for unsupervised feature for finding succinct, a little above high - level Representation of inputs, and it has successfully given a way for Deep learning. Our objective is to use High…
The two primary approaches for high-dimensional regression problems are sparse methods (e.g., best subset selection, which uses the L0-norm in the penalty) and ensemble methods (e.g., random forests). Although sparse methods typically yield…
A common task in inverse problems and imaging is finding a solution that is sparse, in the sense that most of its components vanish. In the framework of compressed sensing, general results guaranteeing exact recovery have been proven. In…
The Lasso has become a benchmark data analysis procedure, and numerous variants have been proposed in the literature. Although the Lasso formulations are stated so that overall prediction error is optimized, no full control over the…
We study the problem of multivariate regression where the data are naturally grouped, and a regression matrix is to be estimated for each group. We propose an approach in which a dictionary of low rank parameter matrices is estimated across…
Sparse data models, where data is assumed to be well represented as a linear combination of a few elements from a dictionary, have gained considerable attention in recent years, and their use has led to state-of-the-art results in many…
Sparse linear regression is a vast field and there are many different algorithms available to build models. Two new papers published in Statistical Science study the comparative performance of several sparse regression methodologies,…
We propose a new sparse regression method called the component lasso, based on a simple idea. The method uses the connected-components structure of the sample covariance matrix to split the problem into smaller ones. It then solves the…
Scaled sparse linear regression jointly estimates the regression coefficients and noise level in a linear model. It chooses an equilibrium with a sparse regression method by iteratively estimating the noise level via the mean residual…
Standard high-dimensional regression methods assume that the underlying coefficient vector is sparse. This might not be true in some cases, in particular in presence of hidden, confounding variables. Such hidden confounding can be…
We consider the problems of estimation and selection of parameters endowed with a known group structure, when the groups are assumed to be sign-coherent, that is, gathering either nonnegative, nonpositive or null parameters. To tackle this…
It is well-known that the statistical performance of Lasso can suffer significantly when the covariates of interest have strong correlations. In particular, the prediction error of Lasso becomes much worse than computationally inefficient…
Joint sparsity offers powerful structural cues for feature selection, especially for variables that are expected to demonstrate a "grouped" behavior. Such behavior is commonly modeled via group-lasso, multitask lasso, and related methods…
We present a comprehensive framework for structured sparse coding and modeling extending the recent ideas of using learnable fast regressors to approximate exact sparse codes. For this purpose, we develop a novel block-coordinate proximal…
The popular Lasso approach for sparse estimation can be derived via marginalization of a joint density associated with a particular stochastic model. A different marginalization of the same probabilistic model leads to a different…
Solving l1 regularized optimization problems is common in the fields of computational biology, signal processing and machine learning. Such l1 regularization is utilized to find sparse minimizers of convex functions. A well-known example is…