616 research outputs found
DC Proximal Newton for Non-Convex Optimization Problems
We introduce a novel algorithm for solving learning problems where both the
loss function and the regularizer are non-convex but belong to the class of
difference of convex (DC) functions. Our contribution is a new general purpose
proximal Newton algorithm that is able to deal with such a situation. The
algorithm consists in obtaining a descent direction from an approximation of
the loss function and then in performing a line search to ensure sufficient
descent. A theoretical analysis is provided showing that the iterates of the
proposed algorithm {admit} as limit points stationary points of the DC
objective function. Numerical experiments show that our approach is more
efficient than current state of the art for a problem with a convex loss
functions and non-convex regularizer. We have also illustrated the benefit of
our algorithm in high-dimensional transductive learning problem where both loss
function and regularizers are non-convex
Simultaneous identification of specifically interacting paralogs and inter-protein contacts by Direct-Coupling Analysis
Understanding protein-protein interactions is central to our understanding of
almost all complex biological processes. Computational tools exploiting rapidly
growing genomic databases to characterize protein-protein interactions are
urgently needed. Such methods should connect multiple scales from evolutionary
conserved interactions between families of homologous proteins, over the
identification of specifically interacting proteins in the case of multiple
paralogs inside a species, down to the prediction of residues being in physical
contact across interaction interfaces. Statistical inference methods detecting
residue-residue coevolution have recently triggered considerable progress in
using sequence data for quaternary protein structure prediction; they require,
however, large joint alignments of homologous protein pairs known to interact.
The generation of such alignments is a complex computational task on its own;
application of coevolutionary modeling has in turn been restricted to proteins
without paralogs, or to bacterial systems with the corresponding coding genes
being co-localized in operons. Here we show that the Direct-Coupling Analysis
of residue coevolution can be extended to connect the different scales, and
simultaneously to match interacting paralogs, to identify inter-protein
residue-residue contacts and to discriminate interacting from noninteracting
families in a multiprotein system. Our results extend the potential
applications of coevolutionary analysis far beyond cases treatable so far.Comment: Main Text 19 pages Supp. Inf. 16 page
Proceedings of the second "international Traveling Workshop on Interactions between Sparse models and Technology" (iTWIST'14)
The implicit objective of the biennial "international - Traveling Workshop on
Interactions between Sparse models and Technology" (iTWIST) is to foster
collaboration between international scientific teams by disseminating ideas
through both specific oral/poster presentations and free discussions. For its
second edition, the iTWIST workshop took place in the medieval and picturesque
town of Namur in Belgium, from Wednesday August 27th till Friday August 29th,
2014. The workshop was conveniently located in "The Arsenal" building within
walking distance of both hotels and town center. iTWIST'14 has gathered about
70 international participants and has featured 9 invited talks, 10 oral
presentations, and 14 posters on the following themes, all related to the
theory, application and generalization of the "sparsity paradigm":
Sparsity-driven data sensing and processing; Union of low dimensional
subspaces; Beyond linear and convex inverse problem; Matrix/manifold/graph
sensing/processing; Blind inverse problems and dictionary learning; Sparsity
and computational neuroscience; Information theory, geometry and randomness;
Complexity/accuracy tradeoffs in numerical methods; Sparsity? What's next?;
Sparse machine learning and inference.Comment: 69 pages, 24 extended abstracts, iTWIST'14 website:
http://sites.google.com/site/itwist1
Spatial CUSUM for Signal Region Detection
Detecting weak clustered signal in spatial data is important but challenging
in applications such as medical image and epidemiology. A more efficient
detection algorithm can provide more precise early warning, and effectively
reduce the decision risk and cost. To date, many methods have been developed to
detect signals with spatial structures. However, most of the existing methods
are either too conservative for weak signals or computationally too intensive.
In this paper, we consider a novel method named Spatial CUSUM (SCUSUM), which
employs the idea of the CUSUM procedure and false discovery rate controlling.
We develop theoretical properties of the method which indicates that
asymptotically SCUSUM can reach high classification accuracy. In the simulation
study, we demonstrate that SCUSUM is sensitive to weak spatial signals. This
new method is applied to a real fMRI dataset as illustration, and more
irregular weak spatial signals are detected in the images compared to some
existing methods, including the conventional FDR, FDR and scan statistics
Group SLOPE Penalized Low-Rank Tensor Regression
This article aims to seek a selection and estimation procedure for a class of
tensor regression problems with multivariate covariates and matrix responses,
which can provide theoretical guarantees for model selection in finite samples.
Considering the frontal slice sparsity and low-rankness inherited in the
coefficient tensor, we formulate the regression procedure as a group SLOPE
penalized low-rank tensor optimization problem based on an orthogonal
decomposition, namely TgSLOPE. This procedure provably controls the newly
introduced tensor group false discovery rate (TgFDR), provided that the
predictor matrix is column-orthogonal. Moreover, we establish the
asymptotically minimax convergence with respect to the TgSLOPE estimate risk.
For efficient problem resolution, we equivalently transform the TgSLOPE problem
into a difference-of-convex (DC) program with the level-coercive objective
function. This allows us to solve the reformulation problem of TgSLOPE by an
efficient proximal DC algorithm (DCA) with global convergence. Numerical
studies conducted on synthetic data and a real human brain connection data
illustrate the efficacy of the proposed TgSLOPE estimation procedure
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