84,041 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
Direct estimation of kinetic parametric images for dynamic PET.
Dynamic positron emission tomography (PET) can monitor spatiotemporal distribution of radiotracer in vivo. The spatiotemporal information can be used to estimate parametric images of radiotracer kinetics that are of physiological and biochemical interests. Direct estimation of parametric images from raw projection data allows accurate noise modeling and has been shown to offer better image quality than conventional indirect methods, which reconstruct a sequence of PET images first and then perform tracer kinetic modeling pixel-by-pixel. Direct reconstruction of parametric images has gained increasing interests with the advances in computing hardware. Many direct reconstruction algorithms have been developed for different kinetic models. In this paper we review the recent progress in the development of direct reconstruction algorithms for parametric image estimation. Algorithms for linear and nonlinear kinetic models are described and their properties are discussed
Stable Feature Selection from Brain sMRI
Neuroimage analysis usually involves learning thousands or even millions of
variables using only a limited number of samples. In this regard, sparse
models, e.g. the lasso, are applied to select the optimal features and achieve
high diagnosis accuracy. The lasso, however, usually results in independent
unstable features. Stability, a manifest of reproducibility of statistical
results subject to reasonable perturbations to data and the model, is an
important focus in statistics, especially in the analysis of high dimensional
data. In this paper, we explore a nonnegative generalized fused lasso model for
stable feature selection in the diagnosis of Alzheimer's disease. In addition
to sparsity, our model incorporates two important pathological priors: the
spatial cohesion of lesion voxels and the positive correlation between the
features and the disease labels. To optimize the model, we propose an efficient
algorithm by proving a novel link between total variation and fast network flow
algorithms via conic duality. Experiments show that the proposed nonnegative
model performs much better in exploring the intrinsic structure of data via
selecting stable features compared with other state-of-the-arts
Time resolved tracking of a sound scatterer in a turbulent flow: non-stationary signal analysis and applications
It is known that ultrasound techniques yield non-intrusive measurements of
hydrodynamic flows. For example, the study of the echoes produced by a large
number of particle insonified by pulsed wavetrains has led to a now standard
velocimetry technique. In this paper, we propose to extend the method to the
continuous tracking of one single particle embedded in a complex flow. This
gives a Lagrangian measurement of the fluid motion, which is of importance in
mixing and turbulence studies. The method relies on the ability to resolve in
time the Doppler shift of the sound scattered by the continuously insonfied
particle.
For this signal processing problem two classes of approaches are used:
time-frequency analysis and parametric high resolution methods. In the first
class we consider the spectrogram and reassigned spectrogram, and we apply it
to detect the motion of a small bead settling in a fluid at rest. In more
non-stationary turbulent flows where methods in the second class are more
robust, we have adapted an Approximated Maximum Likelihood technique coupled
with a generalized Kalman filter.Comment: 16 pages 9 figure
Optimal web-scale tiering as a flow problem
We present a fast online solver for large scale parametric max-flow problems as they occur in portfolio optimization, inventory management, computer vision, and logistics. Our algorithm solves an integer linear program in an online fashion. It exploits total unimodularity of the constraint matrix and a Lagrangian relaxation to solve the problem as a convex online game. The algorithm generates approximate solutions of max-flow problems by performing stochastic gradient descent on a set of flows. We apply the algorithm to optimize tier arrangement of over 84 million web pages on a layered set of caches to serve an incoming query stream optimally
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