26,998 research outputs found
Network Flow Algorithms for Structured Sparsity
We consider a class of learning problems that involve a structured
sparsity-inducing norm defined as the sum of -norms over groups of
variables. Whereas a lot of effort has been put in developing fast optimization
methods when the groups are disjoint or embedded in a specific hierarchical
structure, we address here the case of general overlapping groups. To this end,
we show that the corresponding optimization problem is related to network flow
optimization. More precisely, the proximal problem associated with the norm we
consider is dual to a quadratic min-cost flow problem. We propose an efficient
procedure which computes its solution exactly in polynomial time. Our algorithm
scales up to millions of variables, and opens up a whole new range of
applications for structured sparse models. We present several experiments on
image and video data, demonstrating the applicability and scalability of our
approach for various problems.Comment: accepted for publication in Adv. Neural Information Processing
Systems, 201
Potts model, parametric maxflow and k-submodular functions
The problem of minimizing the Potts energy function frequently occurs in
computer vision applications. One way to tackle this NP-hard problem was
proposed by Kovtun [19,20]. It identifies a part of an optimal solution by
running maxflow computations, where is the number of labels. The number
of "labeled" pixels can be significant in some applications, e.g. 50-93% in our
tests for stereo. We show how to reduce the runtime to maxflow
computations (or one {\em parametric maxflow} computation). Furthermore, the
output of our algorithm allows to speed-up the subsequent alpha expansion for
the unlabeled part, or can be used as it is for time-critical applications.
To derive our technique, we generalize the algorithm of Felzenszwalb et al.
[7] for {\em Tree Metrics}. We also show a connection to {\em -submodular
functions} from combinatorial optimization, and discuss {\em -submodular
relaxations} for general energy functions.Comment: Accepted to ICCV 201
Aerodynamic Optimization of High-Speed Trains Nose using a Genetic Algorithm and Artificial Neural Network
An aerodynamic optimization of the train aerodynamic characteristics in term of front wind action sensitivity is carried out in this paper. In particular, a genetic algorithm (GA) is used to perform a shape optimization study of a high-speed train nose. The nose is parametrically defined via Bézier Curves, including a wider range of geometries in the design space as possible optimal solutions. Using a GA, the main disadvantage to deal with is the large number of evaluations need before finding such optimal. Here it is proposed the use of metamodels to replace Navier-Stokes solver. Among all the posibilities, Rsponse Surface Models and Artificial Neural Networks (ANN) are considered. Best results of prediction and generalization are obtained with ANN and those are applied in GA code. The paper shows the feasibility of using GA in combination with ANN for this problem, and solutions achieved are included
Accelerating Permutation Testing in Voxel-wise Analysis through Subspace Tracking: A new plugin for SnPM
Permutation testing is a non-parametric method for obtaining the max null
distribution used to compute corrected -values that provide strong control
of false positives. In neuroimaging, however, the computational burden of
running such an algorithm can be significant. We find that by viewing the
permutation testing procedure as the construction of a very large permutation
testing matrix, , one can exploit structural properties derived from the
data and the test statistics to reduce the runtime under certain conditions. In
particular, we see that is low-rank plus a low-variance residual. This
makes a good candidate for low-rank matrix completion, where only a very
small number of entries of ( of all entries in our experiments)
have to be computed to obtain a good estimate. Based on this observation, we
present RapidPT, an algorithm that efficiently recovers the max null
distribution commonly obtained through regular permutation testing in
voxel-wise analysis. We present an extensive validation on a synthetic dataset
and four varying sized datasets against two baselines: Statistical
NonParametric Mapping (SnPM13) and a standard permutation testing
implementation (referred as NaivePT). We find that RapidPT achieves its best
runtime performance on medium sized datasets (), with
speedups of 1.5x - 38x (vs. SnPM13) and 20x-1000x (vs. NaivePT). For larger
datasets () RapidPT outperforms NaivePT (6x - 200x) on all
datasets, and provides large speedups over SnPM13 when more than 10000
permutations (2x - 15x) are needed. The implementation is a standalone toolbox
and also integrated within SnPM13, able to leverage multi-core architectures
when available.Comment: 36 pages, 16 figure
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