8,631 research outputs found
Computing parametric ranking models via rank-breaking. In
Abstract Rank breaking is a methodology introduced by Azar
Minimax-optimal Inference from Partial Rankings
This paper studies the problem of inferring a global preference based on the
partial rankings provided by many users over different subsets of items
according to the Plackett-Luce model. A question of particular interest is how
to optimally assign items to users for ranking and how many item assignments
are needed to achieve a target estimation error. For a given assignment of
items to users, we first derive an oracle lower bound of the estimation error
that holds even for the more general Thurstone models. Then we show that the
Cram\'er-Rao lower bound and our upper bounds inversely depend on the spectral
gap of the Laplacian of an appropriately defined comparison graph. When the
system is allowed to choose the item assignment, we propose a random assignment
scheme. Our oracle lower bound and upper bounds imply that it is
minimax-optimal up to a logarithmic factor among all assignment schemes and the
lower bound can be achieved by the maximum likelihood estimator as well as
popular rank-breaking schemes that decompose partial rankings into pairwise
comparisons. The numerical experiments corroborate our theoretical findings.Comment: 16 pages, 2 figure
Generalized Method-of-Moments for Rank Aggregation
In this paper we propose a class of efficient Generalized Method-of-Moments(GMM) algorithms for computing parameters of the Plackett-Luce model, where the data consists of full rankings over alternatives. Our technique is based on breaking the full rankings into pairwise comparisons, and then computing parameters that satisfy a set of generalized moment conditions. We identify conditions for the output of GMM to be unique, and identify a general class of consistent and inconsistent breakings. We then show by theory and experiments that our algorithms run significantly faster than the classical Minorize-Maximization (MM) algorithm, while achieving competitive statistical efficiency.Engineering and Applied SciencesStatistic
Functional Generative Design: An Evolutionary Approach to 3D-Printing
Consumer-grade printers are widely available, but their ability to print
complex objects is limited. Therefore, new designs need to be discovered that
serve the same function, but are printable. A representative such problem is to
produce a working, reliable mechanical spring. The proposed methodology for
discovering solutions to this problem consists of three components: First, an
effective search space is learned through a variational autoencoder (VAE);
second, a surrogate model for functional designs is built; and third, a genetic
algorithm is used to simultaneously update the hyperparameters of the surrogate
and to optimize the designs using the updated surrogate. Using a car-launcher
mechanism as a test domain, spring designs were 3D-printed and evaluated to
update the surrogate model. Two experiments were then performed: First, the
initial set of designs for the surrogate-based optimizer was selected randomly
from the training set that was used for training the VAE model, which resulted
in an exploitative search behavior. On the other hand, in the second
experiment, the initial set was composed of more uniformly selected designs
from the same training set and a more explorative search behavior was observed.
Both of the experiments showed that the methodology generates interesting,
successful, and reliable spring geometries robust to the noise inherent in the
3D printing process. The methodology can be generalized to other functional
design problems, thus making consumer-grade 3D printing more versatile.Comment: 8 pages, 12 figures, GECCO'1
Complex Networks from Classical to Quantum
Recent progress in applying complex network theory to problems in quantum
information has resulted in a beneficial crossover. Complex network methods
have successfully been applied to transport and entanglement models while
information physics is setting the stage for a theory of complex systems with
quantum information-inspired methods. Novel quantum induced effects have been
predicted in random graphs---where edges represent entangled links---and
quantum computer algorithms have been proposed to offer enhancement for several
network problems. Here we review the results at the cutting edge, pinpointing
the similarities and the differences found at the intersection of these two
fields.Comment: 12 pages, 4 figures, REVTeX 4-1, accepted versio
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