15,058 research outputs found
Proximal Methods for Hierarchical Sparse Coding
Sparse coding consists in representing signals as sparse linear combinations
of atoms selected from a dictionary. We consider an extension of this framework
where the atoms are further assumed to be embedded in a tree. This is achieved
using a recently introduced tree-structured sparse regularization norm, which
has proven useful in several applications. This norm leads to regularized
problems that are difficult to optimize, and we propose in this paper efficient
algorithms for solving them. More precisely, we show that the proximal operator
associated with this norm is computable exactly via a dual approach that can be
viewed as the composition of elementary proximal operators. Our procedure has a
complexity linear, or close to linear, in the number of atoms, and allows the
use of accelerated gradient techniques to solve the tree-structured sparse
approximation problem at the same computational cost as traditional ones using
the L1-norm. Our method is efficient and scales gracefully to millions of
variables, which we illustrate in two types of applications: first, we consider
fixed hierarchical dictionaries of wavelets to denoise natural images. Then, we
apply our optimization tools in the context of dictionary learning, where
learned dictionary elements naturally organize in a prespecified arborescent
structure, leading to a better performance in reconstruction of natural image
patches. When applied to text documents, our method learns hierarchies of
topics, thus providing a competitive alternative to probabilistic topic models
Family Interaction Styles of Children with Depressive Disorders, Schizophrenia-Spectrum Disorders, and Normal Controls
Family interaction processes during a problem-solving task were examined in children with depressive disorders, children with schizophrenia-spectrum disorders, and a normal control group of community children screened for the absence of psychiatric disorder. Major findings were: a) children with depressive disorders were more likely than children with schizophrenia-spectrum disorders and children with no psychiatric disorder to direct guilt-inducing comments toward their parents; and b) parents of children with schizophrenia-spectrum disorders were more likely to direct harsh critical comments toward the child than were parents of depressed children or parents of normal controls. In addition, children\u27s and mothers\u27 use of benign criticism was linked, while children\u27s harsh criticism was associated with intrusion from the father, and children\u27s self-denigrating comments were related to specific paternal criticism. Implications of these results for understanding transactional processes associated with childhood-onset depressive and schizophrenia-spectrum disorders are discussed
Sparse Modeling for Image and Vision Processing
In recent years, a large amount of multi-disciplinary research has been
conducted on sparse models and their applications. In statistics and machine
learning, the sparsity principle is used to perform model selection---that is,
automatically selecting a simple model among a large collection of them. In
signal processing, sparse coding consists of representing data with linear
combinations of a few dictionary elements. Subsequently, the corresponding
tools have been widely adopted by several scientific communities such as
neuroscience, bioinformatics, or computer vision. The goal of this monograph is
to offer a self-contained view of sparse modeling for visual recognition and
image processing. More specifically, we focus on applications where the
dictionary is learned and adapted to data, yielding a compact representation
that has been successful in various contexts.Comment: 205 pages, to appear in Foundations and Trends in Computer Graphics
and Visio
Optimization with Sparsity-Inducing Penalties
Sparse estimation methods are aimed at using or obtaining parsimonious
representations of data or models. They were first dedicated to linear variable
selection but numerous extensions have now emerged such as structured sparsity
or kernel selection. It turns out that many of the related estimation problems
can be cast as convex optimization problems by regularizing the empirical risk
with appropriate non-smooth norms. The goal of this paper is to present from a
general perspective optimization tools and techniques dedicated to such
sparsity-inducing penalties. We cover proximal methods, block-coordinate
descent, reweighted -penalized techniques, working-set and homotopy
methods, as well as non-convex formulations and extensions, and provide an
extensive set of experiments to compare various algorithms from a computational
point of view
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