5,009 research outputs found
Separable Convex Optimization with Nested Lower and Upper Constraints
We study a convex resource allocation problem in which lower and upper bounds
are imposed on partial sums of allocations. This model is linked to a large
range of applications, including production planning, speed optimization,
stratified sampling, support vector machines, portfolio management, and
telecommunications. We propose an efficient gradient-free divide-and-conquer
algorithm, which uses monotonicity arguments to generate valid bounds from the
recursive calls, and eliminate linking constraints based on the information
from sub-problems. This algorithm does not need strict convexity or
differentiability. It produces an -approximate solution for the
continuous problem in time
and an integer solution in time, where is
the number of decision variables, is the number of constraints, and is
the resource bound. A complexity of is also achieved
for the linear and quadratic cases. These are the best complexities known to
date for this important problem class. Our experimental analyses confirm the
good performance of the method, which produces optimal solutions for problems
with up to 1,000,000 variables in a few seconds. Promising applications to the
support vector ordinal regression problem are also investigated
Scalable Sparse Subspace Clustering by Orthogonal Matching Pursuit
Subspace clustering methods based on , or nuclear norm
regularization have become very popular due to their simplicity, theoretical
guarantees and empirical success. However, the choice of the regularizer can
greatly impact both theory and practice. For instance, regularization
is guaranteed to give a subspace-preserving affinity (i.e., there are no
connections between points from different subspaces) under broad conditions
(e.g., arbitrary subspaces and corrupted data). However, it requires solving a
large scale convex optimization problem. On the other hand, and
nuclear norm regularization provide efficient closed form solutions, but
require very strong assumptions to guarantee a subspace-preserving affinity,
e.g., independent subspaces and uncorrupted data. In this paper we study a
subspace clustering method based on orthogonal matching pursuit. We show that
the method is both computationally efficient and guaranteed to give a
subspace-preserving affinity under broad conditions. Experiments on synthetic
data verify our theoretical analysis, and applications in handwritten digit and
face clustering show that our approach achieves the best trade off between
accuracy and efficiency.Comment: 13 pages, 1 figure, 2 tables. Accepted to CVPR 2016 as an oral
presentatio
Approximate transformations and robust manipulation of bipartite pure state entanglement
We analyze approximate transformations of pure entangled quantum states by
local operations and classical communication, finding explicit conversion
strategies which optimize the fidelity of transformation. These results allow
us to determine the most faithful teleportation strategy via an initially
shared partially entangled pure state. They also show that procedures for
entanglement manipulation such as entanglement catalysis [Jonathan and Plenio,
Phys. Rev. Lett. 83, 3566 (1999)] are robust against perturbation of the states
involved, and motivate the notion of non-local fidelity, which quantifies the
difference in the entangled properties of two quantum states.Comment: 11 pages, 4 figure
Inertial Load Compensation by a Model Spinal Circuit During Single Joint Movement
Office of Naval Research (N00014-92-J-1309); CONACYT (Mexico) (63462
Los transgénicos en la alimentación
Contrariamente a lo que mucha gente piensa, emplear genética en la
alimentación y la nutrición no es nuevo. Desde hace 12000 años, en los
albores de la agricultura y la ganadería, el hombre, ha mejorado las razas
de animales de granja y las variedades vegetales comestibles utilizando
técnicas genéticas (García Olmedo, 2009). Comenzó domesticando estos
organismos y acabó mejorándolos mediante el empleo de genética
(Reichholf, 2009). Para ello utilizó varias técnicas. De entre todas ellas las
más utilizadas han sido la hibridación, conocida como cruce sexual, y la
aparición de mutantes espontáneos, también llamada variabilidad natural
Oracle Based Active Set Algorithm for Scalable Elastic Net Subspace Clustering
State-of-the-art subspace clustering methods are based on expressing each
data point as a linear combination of other data points while regularizing the
matrix of coefficients with , or nuclear norms.
regularization is guaranteed to give a subspace-preserving affinity (i.e.,
there are no connections between points from different subspaces) under broad
theoretical conditions, but the clusters may not be connected. and
nuclear norm regularization often improve connectivity, but give a
subspace-preserving affinity only for independent subspaces. Mixed ,
and nuclear norm regularizations offer a balance between the
subspace-preserving and connectedness properties, but this comes at the cost of
increased computational complexity. This paper studies the geometry of the
elastic net regularizer (a mixture of the and norms) and uses
it to derive a provably correct and scalable active set method for finding the
optimal coefficients. Our geometric analysis also provides a theoretical
justification and a geometric interpretation for the balance between the
connectedness (due to regularization) and subspace-preserving (due to
regularization) properties for elastic net subspace clustering. Our
experiments show that the proposed active set method not only achieves
state-of-the-art clustering performance, but also efficiently handles
large-scale datasets.Comment: 15 pages, 6 figures, accepted to CVPR 2016 for oral presentatio
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