6,714 research outputs found
Convex Optimization for Binary Classifier Aggregation in Multiclass Problems
Multiclass problems are often decomposed into multiple binary problems that
are solved by individual binary classifiers whose results are integrated into a
final answer. Various methods, including all-pairs (APs), one-versus-all (OVA),
and error correcting output code (ECOC), have been studied, to decompose
multiclass problems into binary problems. However, little study has been made
to optimally aggregate binary problems to determine a final answer to the
multiclass problem. In this paper we present a convex optimization method for
an optimal aggregation of binary classifiers to estimate class membership
probabilities in multiclass problems. We model the class membership probability
as a softmax function which takes a conic combination of discrepancies induced
by individual binary classifiers, as an input. With this model, we formulate
the regularized maximum likelihood estimation as a convex optimization problem,
which is solved by the primal-dual interior point method. Connections of our
method to large margin classifiers are presented, showing that the large margin
formulation can be considered as a limiting case of our convex formulation.
Numerical experiments on synthetic and real-world data sets demonstrate that
our method outperforms existing aggregation methods as well as direct methods,
in terms of the classification accuracy and the quality of class membership
probability estimates.Comment: Appeared in Proceedings of the 2014 SIAM International Conference on
Data Mining (SDM 2014
Wireless Data Acquisition for Edge Learning: Data-Importance Aware Retransmission
By deploying machine-learning algorithms at the network edge, edge learning
can leverage the enormous real-time data generated by billions of mobile
devices to train AI models, which enable intelligent mobile applications. In
this emerging research area, one key direction is to efficiently utilize radio
resources for wireless data acquisition to minimize the latency of executing a
learning task at an edge server. Along this direction, we consider the specific
problem of retransmission decision in each communication round to ensure both
reliability and quantity of those training data for accelerating model
convergence. To solve the problem, a new retransmission protocol called
data-importance aware automatic-repeat-request (importance ARQ) is proposed.
Unlike the classic ARQ focusing merely on reliability, importance ARQ
selectively retransmits a data sample based on its uncertainty which helps
learning and can be measured using the model under training. Underpinning the
proposed protocol is a derived elegant communication-learning relation between
two corresponding metrics, i.e., signal-to-noise ratio (SNR) and data
uncertainty. This relation facilitates the design of a simple threshold based
policy for importance ARQ. The policy is first derived based on the classic
classifier model of support vector machine (SVM), where the uncertainty of a
data sample is measured by its distance to the decision boundary. The policy is
then extended to the more complex model of convolutional neural networks (CNN)
where data uncertainty is measured by entropy. Extensive experiments have been
conducted for both the SVM and CNN using real datasets with balanced and
imbalanced distributions. Experimental results demonstrate that importance ARQ
effectively copes with channel fading and noise in wireless data acquisition to
achieve faster model convergence than the conventional channel-aware ARQ.Comment: This is an updated version: 1) extension to general classifiers; 2)
consideration of imbalanced classification in the experiments. Submitted to
IEEE Journal for possible publicatio
Disparity and Optical Flow Partitioning Using Extended Potts Priors
This paper addresses the problems of disparity and optical flow partitioning
based on the brightness invariance assumption. We investigate new variational
approaches to these problems with Potts priors and possibly box constraints.
For the optical flow partitioning, our model includes vector-valued data and an
adapted Potts regularizer. Using the notation of asymptotically level stable
functions we prove the existence of global minimizers of our functionals. We
propose a modified alternating direction method of minimizers. This iterative
algorithm requires the computation of global minimizers of classical univariate
Potts problems which can be done efficiently by dynamic programming. We prove
that the algorithm converges both for the constrained and unconstrained
problems. Numerical examples demonstrate the very good performance of our
partitioning method
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