1,047 research outputs found
Hypercubes and Compromise Values for Cooperative Fuzzy Games
AMS classification: 90D12; 03E72;cooperative games;Compromise values;Core;Fuzzy coalitions;Fuzzy games;Hypercubes;Path solutions;Weber set
Harmonious Hilbert curves and other extradimensional space-filling curves
This paper introduces a new way of generalizing Hilbert's two-dimensional
space-filling curve to arbitrary dimensions. The new curves, called harmonious
Hilbert curves, have the unique property that for any d' < d, the d-dimensional
curve is compatible with the d'-dimensional curve with respect to the order in
which the curves visit the points of any d'-dimensional axis-parallel space
that contains the origin. Similar generalizations to arbitrary dimensions are
described for several variants of Peano's curve (the original Peano curve, the
coil curve, the half-coil curve, and the Meurthe curve). The d-dimensional
harmonious Hilbert curves and the Meurthe curves have neutral orientation: as
compared to the curve as a whole, arbitrary pieces of the curve have each of d!
possible rotations with equal probability. Thus one could say these curves are
`statistically invariant' under rotation---unlike the Peano curves, the coil
curves, the half-coil curves, and the familiar generalization of Hilbert curves
by Butz and Moore.
In addition, prompted by an application in the construction of R-trees, this
paper shows how to construct a 2d-dimensional generalized Hilbert or Peano
curve that traverses the points of a certain d-dimensional diagonally placed
subspace in the order of a given d-dimensional generalized Hilbert or Peano
curve.
Pseudocode is provided for comparison operators based on the curves presented
in this paper.Comment: 40 pages, 10 figures, pseudocode include
Inference Based on Conditional Moment Inequalities
In this paper, we propose an instrumental variable approach to constructing confidence sets (CS's) for the true parameter in models defined by conditional moment inequalities/equalities. We show that by properly choosing instrument functions, one can transform conditional moment inequalities/equalities into unconditional ones without losing identification power. Based on the unconditional moment inequalities/equalities, we construct CS's by inverting Cramer-von Mises-type or Kolmogorov-Smirnov-type tests. Critical values are obtained using generalized moment selection (GMS) procedures. We show that the proposed CS's have correct uniform asymptotic coverage probabilities. New methods are required to establish these results because an infinite-dimensional nuisance parameter affects the asymptotic distributions. We show that the tests considered are consistent against all fixed alternatives and have power against some n^{-1/2}-local alternatives, though not all such alternatives. Monte Carlo simulations for three different models show that the methods perform well in finite samples.Asymptotic size, asymptotic power, conditional moment inequalities, confidence set, Cramer-von Mises, generalized moment selection, Kolmogorov-Smirnov, moment inequalities
Hypercubes and compromise values for cooperative fuzzy games
90D12;03E72cooperative games
Distributed Online Learning via Cooperative Contextual Bandits
In this paper we propose a novel framework for decentralized, online learning
by many learners. At each moment of time, an instance characterized by a
certain context may arrive to each learner; based on the context, the learner
can select one of its own actions (which gives a reward and provides
information) or request assistance from another learner. In the latter case,
the requester pays a cost and receives the reward but the provider learns the
information. In our framework, learners are modeled as cooperative contextual
bandits. Each learner seeks to maximize the expected reward from its arrivals,
which involves trading off the reward received from its own actions, the
information learned from its own actions, the reward received from the actions
requested of others and the cost paid for these actions - taking into account
what it has learned about the value of assistance from each other learner. We
develop distributed online learning algorithms and provide analytic bounds to
compare the efficiency of these with algorithms with the complete knowledge
(oracle) benchmark (in which the expected reward of every action in every
context is known by every learner). Our estimates show that regret - the loss
incurred by the algorithm - is sublinear in time. Our theoretical framework can
be used in many practical applications including Big Data mining, event
detection in surveillance sensor networks and distributed online recommendation
systems
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