Sparse Regression Using Mixed Norms
نویسنده
چکیده
Mixed norms are used to exploit in an easy way, both structure and sparsity in the framework of regression problems, and introduce implicitly couplings between regression coefficients. Regression is done through optimization problems, and corresponding algorithms are described and analyzed. Beside the classical sparse regression problem, multilayered expansion on unions of dictionaries of signals are also considered. These sparse structured expansions are done subject to an exact reconstruction constraint, using a modified FOCUSS algorithm. When the mixed norms are used in the framework of regularized inverse problem, a thresholded Landweber iteration is used to minimize the corresponding variational problem.
منابع مشابه
Sparsity and persistence: mixed norms provide simple signal models with dependent coefficients
Sparse regression often uses `p norm priors (with p < 2). This paper demonstrates that the introduction of mixed-norms in such contexts allows one to go one step beyond in signal models, and promote some different, structured, forms of sparsity. It is shown that the particular case of the `1,2 and `2,1 norms leads to new group shrinkage operators. Mixed norm priors are shown to be particularly ...
متن کاملA scalable trust-region algorithm with application to mixed-norm regression
We present a new algorithm for minimizing a convex loss-function subject to regularization. Our framework applies to numerous problems in machine learning and statistics; notably, for sparsity-promoting regularizers such as `1 or `1,∞ norms, it enables efficient computation of sparse solutions. Our approach is based on the trust-region framework with nonsmooth objectives, which allows us to bui...
متن کاملPredicting Alzheimer's Disease Cognitive Assessment via Robust Low-Rank Structured Sparse Model
Alzheimer’s disease (AD) is a neurodegenerative disorder with slow onset, which could result in the deterioration of the duration of persistent neurological dysfunction. How to identify the informative longitudinal phenotypic neuroimaging markers and predict cognitive measures are crucial to recognize AD at early stage. Many existing models related imaging measures to cognitive status using reg...
متن کاملRobust Estimation in Linear Regression with Molticollinearity and Sparse Models
One of the factors affecting the statistical analysis of the data is the presence of outliers. The methods which are not affected by the outliers are called robust methods. Robust regression methods are robust estimation methods of regression model parameters in the presence of outliers. Besides outliers, the linear dependency of regressor variables, which is called multicollinearity...
متن کاملBeyond Moore-Penrose Part I: Generalized Inverses that Minimize Matrix Norms
This is the first paper of a two-long series in which we study linear generalized inverses that minimize matrix norms. Such generalized inverses are famously represented by the Moore-Penrose pseudoinverse (MPP) which happens to minimize the Frobenius norm. Freeing up the degrees of freedom associated with Frobenius optimality enables us to promote other interesting properties. In this Part I, w...
متن کامل