138,925 research outputs found
Submodular relaxation for inference in Markov random fields
In this paper we address the problem of finding the most probable state of a
discrete Markov random field (MRF), also known as the MRF energy minimization
problem. The task is known to be NP-hard in general and its practical
importance motivates numerous approximate algorithms. We propose a submodular
relaxation approach (SMR) based on a Lagrangian relaxation of the initial
problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR
does not decompose the graph structure of the initial problem but constructs a
submodular energy that is minimized within the Lagrangian relaxation. Our
approach is applicable to both pairwise and high-order MRFs and allows to take
into account global potentials of certain types. We study theoretical
properties of the proposed approach and evaluate it experimentally.Comment: This paper is accepted for publication in IEEE Transactions on
Pattern Analysis and Machine Intelligenc
Thresholded Covering Algorithms for Robust and Max-Min Optimization
The general problem of robust optimization is this: one of several possible
scenarios will appear tomorrow, but things are more expensive tomorrow than
they are today. What should you anticipatorily buy today, so that the
worst-case cost (summed over both days) is minimized? Feige et al. and
Khandekar et al. considered the k-robust model where the possible outcomes
tomorrow are given by all demand-subsets of size k, and gave algorithms for the
set cover problem, and the Steiner tree and facility location problems in this
model, respectively.
In this paper, we give the following simple and intuitive template for
k-robust problems: "having built some anticipatory solution, if there exists a
single demand whose augmentation cost is larger than some threshold, augment
the anticipatory solution to cover this demand as well, and repeat". In this
paper we show that this template gives us improved approximation algorithms for
k-robust Steiner tree and set cover, and the first approximation algorithms for
k-robust Steiner forest, minimum-cut and multicut. All our approximation ratios
(except for multicut) are almost best possible.
As a by-product of our techniques, we also get algorithms for max-min
problems of the form: "given a covering problem instance, which k of the
elements are costliest to cover?".Comment: 24 page
Robust Linear Precoder Design for Multi-cell Downlink Transmission
Coordinated information processing by the base stations of multi-cell
wireless networks enhances the overall quality of communication in the network.
Such coordinations for optimizing any desired network-wide quality of service
(QoS) necessitate the base stations to acquire and share some channel state
information (CSI). With perfect knowledge of channel states, the base stations
can adjust their transmissions for achieving a network-wise QoS optimality. In
practice, however, the CSI can be obtained only imperfectly. As a result, due
to the uncertainties involved, the network is not guaranteed to benefit from a
globally optimal QoS. Nevertheless, if the channel estimation perturbations are
confined within bounded regions, the QoS measure will also lie within a bounded
region. Therefore, by exploiting the notion of robustness in the worst-case
sense some worst-case QoS guarantees for the network can be asserted. We adopt
a popular model for noisy channel estimates that assumes that estimation noise
terms lie within known hyper-spheres. We aim to design linear transceivers that
optimize a worst-case QoS measure in downlink transmissions. In particular, we
focus on maximizing the worst-case weighted sum-rate of the network and the
minimum worst-case rate of the network. For obtaining such transceiver designs,
we offer several centralized (fully cooperative) and distributed (limited
cooperation) algorithms which entail different levels of complexity and
information exchange among the base stations.Comment: 38 Pages, 7 Figures, To appear in the IEEE Transactions on Signal
Processin
Kernel Ellipsoidal Trimming
Ellipsoid estimation is an issue of primary importance in many practical areas such as control, system identification, visual/audio tracking, experimental design, data mining, robust statistics and novelty/outlier detection. This paper presents a new method of kernel information matrix ellipsoid estimation (KIMEE) that finds an ellipsoid in a kernel defined feature space based on a centered information matrix. Although the method is very general and can be applied to many of the aforementioned problems, the main focus in this paper is the problem of novelty or outlier detection associated with fault detection. A simple iterative algorithm based on Titterington's minimum volume ellipsoid method is proposed for practical implementation. The KIMEE method demonstrates very good performance on a set of real-life and simulated datasets compared with support vector machine methods
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