116,157 research outputs found
Cheaper and Better: Selecting Good Workers for Crowdsourcing
Crowdsourcing provides a popular paradigm for data collection at scale. We
study the problem of selecting subsets of workers from a given worker pool to
maximize the accuracy under a budget constraint. One natural question is
whether we should hire as many workers as the budget allows, or restrict on a
small number of top-quality workers. By theoretically analyzing the error rate
of a typical setting in crowdsourcing, we frame the worker selection problem
into a combinatorial optimization problem and propose an algorithm to solve it
efficiently. Empirical results on both simulated and real-world datasets show
that our algorithm is able to select a small number of high-quality workers,
and performs as good as, sometimes even better than, the much larger crowds as
the budget allows
Net and Prune: A Linear Time Algorithm for Euclidean Distance Problems
We provide a general framework for getting expected linear time constant
factor approximations (and in many cases FPTAS's) to several well known
problems in Computational Geometry, such as -center clustering and farthest
nearest neighbor. The new approach is robust to variations in the input
problem, and yet it is simple, elegant and practical. In particular, many of
these well studied problems which fit easily into our framework, either
previously had no linear time approximation algorithm, or required rather
involved algorithms and analysis. A short list of the problems we consider
include farthest nearest neighbor, -center clustering, smallest disk
enclosing points, th largest distance, th smallest -nearest
neighbor distance, th heaviest edge in the MST and other spanning forest
type problems, problems involving upward closed set systems, and more. Finally,
we show how to extend our framework such that the linear running time bound
holds with high probability
Precoder Design for Physical Layer Multicasting
This paper studies the instantaneous rate maximization and the weighted sum
delay minimization problems over a K-user multicast channel, where multiple
antennas are available at the transmitter as well as at all the receivers.
Motivated by the degree of freedom optimality and the simplicity offered by
linear precoding schemes, we consider the design of linear precoders using the
aforementioned two criteria. We first consider the scenario wherein the linear
precoder can be any complex-valued matrix subject to rank and power
constraints. We propose cyclic alternating ascent based precoder design
algorithms and establish their convergence to respective stationary points.
Simulation results reveal that our proposed algorithms considerably outperform
known competing solutions. We then consider a scenario in which the linear
precoder can be formed by selecting and concatenating precoders from a given
finite codebook of precoding matrices, subject to rank and power constraints.
We show that under this scenario, the instantaneous rate maximization problem
is equivalent to a robust submodular maximization problem which is strongly NP
hard. We propose a deterministic approximation algorithm and show that it
yields a bicriteria approximation. For the weighted sum delay minimization
problem we propose a simple deterministic greedy algorithm, which at each step
entails approximately maximizing a submodular set function subject to multiple
knapsack constraints, and establish its performance guarantee.Comment: 37 pages, 8 figures, submitted to IEEE Trans. Signal Pro
On the Minimization of Convex Functionals of Probability Distributions Under Band Constraints
The problem of minimizing convex functionals of probability distributions is
solved under the assumption that the density of every distribution is bounded
from above and below. A system of sufficient and necessary first-order
optimality conditions as well as a bound on the optimality gap of feasible
candidate solutions are derived. Based on these results, two numerical
algorithms are proposed that iteratively solve the system of optimality
conditions on a grid of discrete points. Both algorithms use a block coordinate
descent strategy and terminate once the optimality gap falls below the desired
tolerance. While the first algorithm is conceptually simpler and more
efficient, it is not guaranteed to converge for objective functions that are
not strictly convex. This shortcoming is overcome in the second algorithm,
which uses an additional outer proximal iteration, and, which is proven to
converge under mild assumptions. Two examples are given to demonstrate the
theoretical usefulness of the optimality conditions as well as the high
efficiency and accuracy of the proposed numerical algorithms.Comment: 13 pages, 5 figures, 2 tables, published in the IEEE Transactions on
Signal Processing. In previous versions, the example in Section VI.B
contained some mistakes and inaccuracies, which have been fixed in this
versio
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