1,105 research outputs found
Fast learning rate of multiple kernel learning: Trade-off between sparsity and smoothness
We investigate the learning rate of multiple kernel learning (MKL) with
and elastic-net regularizations. The elastic-net regularization is a
composition of an -regularizer for inducing the sparsity and an
-regularizer for controlling the smoothness. We focus on a sparse
setting where the total number of kernels is large, but the number of nonzero
components of the ground truth is relatively small, and show sharper
convergence rates than the learning rates have ever shown for both and
elastic-net regularizations. Our analysis reveals some relations between the
choice of a regularization function and the performance. If the ground truth is
smooth, we show a faster convergence rate for the elastic-net regularization
with less conditions than -regularization; otherwise, a faster
convergence rate for the -regularization is shown.Comment: Published in at http://dx.doi.org/10.1214/13-AOS1095 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org). arXiv admin note: text overlap with
arXiv:1103.043
Task Selection for Bandit-Based Task Assignment in Heterogeneous Crowdsourcing
Task selection (picking an appropriate labeling task) and worker selection
(assigning the labeling task to a suitable worker) are two major challenges in
task assignment for crowdsourcing. Recently, worker selection has been
successfully addressed by the bandit-based task assignment (BBTA) method, while
task selection has not been thoroughly investigated yet. In this paper, we
experimentally compare several task selection strategies borrowed from active
learning literature, and show that the least confidence strategy significantly
improves the performance of task assignment in crowdsourcing.Comment: arXiv admin note: substantial text overlap with arXiv:1507.0580
Super-Linear Convergence of Dual Augmented-Lagrangian Algorithm for Sparsity Regularized Estimation
We analyze the convergence behaviour of a recently proposed algorithm for
regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is
based on a new interpretation of DAL as a proximal minimization algorithm. We
theoretically show under some conditions that DAL converges super-linearly in a
non-asymptotic and global sense. Due to a special modelling of sparse
estimation problems in the context of machine learning, the assumptions we make
are milder and more natural than those made in conventional analysis of
augmented Lagrangian algorithms. In addition, the new interpretation enables us
to generalize DAL to wide varieties of sparse estimation problems. We
experimentally confirm our analysis in a large scale -regularized
logistic regression problem and extensively compare the efficiency of DAL
algorithm to previously proposed algorithms on both synthetic and benchmark
datasets.Comment: 51 pages, 9 figure
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