32,316 research outputs found
Multiple kernel contraction
This paper focuses on the extension of AGM that allows change for a belief
base by a set of sentences instead of a single sentence. In [FH94], Fuhrmann and Hansson
presented an axiomatic for Multiple Contraction and a construction based on the AGM
Partial Meet Contraction. We propose for their model another way to construct functions:
Multiple Kernel Contraction, that is a modification of Kernel Contraction, proposed by
Hansson [Han94] to construct classical AGM contractions and belief base contractions.
This construction works out the unsolved problem pointed out by Hansson in [Han99, pp.
369].info:eu-repo/semantics/publishedVersio
Fourth moment theorems on the Poisson space: analytic statements via product formulae
We prove necessary and sufficient conditions for the asymptotic normality of
multiple integrals with respect to a Poisson measure on a general measure
space, expressed both in terms of norms of contraction kernels and of variances
of carr\'e-du-champ operators. Our results substantially complete the fourth
moment theorems recently obtained by D\"obler and Peccati (2018) and D\"obler,
Vidotto and Zheng (2018). An important tool for achieving our goals is a novel
product formula for multiple integrals under minimal conditions.Comment: 14 page
Parameterized Approximation Schemes for Steiner Trees with Small Number of Steiner Vertices
We study the Steiner Tree problem, in which a set of terminal vertices needs
to be connected in the cheapest possible way in an edge-weighted graph. This
problem has been extensively studied from the viewpoint of approximation and
also parametrization. In particular, on one hand Steiner Tree is known to be
APX-hard, and W[2]-hard on the other, if parameterized by the number of
non-terminals (Steiner vertices) in the optimum solution. In contrast to this
we give an efficient parameterized approximation scheme (EPAS), which
circumvents both hardness results. Moreover, our methods imply the existence of
a polynomial size approximate kernelization scheme (PSAKS) for the considered
parameter.
We further study the parameterized approximability of other variants of
Steiner Tree, such as Directed Steiner Tree and Steiner Forest. For neither of
these an EPAS is likely to exist for the studied parameter: for Steiner Forest
an easy observation shows that the problem is APX-hard, even if the input graph
contains no Steiner vertices. For Directed Steiner Tree we prove that
approximating within any function of the studied parameter is W[1]-hard.
Nevertheless, we show that an EPAS exists for Unweighted Directed Steiner Tree,
but a PSAKS does not. We also prove that there is an EPAS and a PSAKS for
Steiner Forest if in addition to the number of Steiner vertices, the number of
connected components of an optimal solution is considered to be a parameter.Comment: 23 pages, 6 figures An extended abstract appeared in proceedings of
STACS 201
Rates of contraction of posterior distributions based on Gaussian process priors
We derive rates of contraction of posterior distributions on nonparametric or
semiparametric models based on Gaussian processes. The rate of contraction is
shown to depend on the position of the true parameter relative to the
reproducing kernel Hilbert space of the Gaussian process and the small ball
probabilities of the Gaussian process. We determine these quantities for a
range of examples of Gaussian priors and in several statistical settings. For
instance, we consider the rate of contraction of the posterior distribution
based on sampling from a smooth density model when the prior models the log
density as a (fractionally integrated) Brownian motion. We also consider
regression with Gaussian errors and smooth classification under a logistic or
probit link function combined with various priors.Comment: Published in at http://dx.doi.org/10.1214/009053607000000613 the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Contains and Inside relationships within combinatorial Pyramids
Irregular pyramids are made of a stack of successively reduced graphs
embedded in the plane. Such pyramids are used within the segmentation framework
to encode a hierarchy of partitions. The different graph models used within the
irregular pyramid framework encode different types of relationships between
regions. This paper compares different graph models used within the irregular
pyramid framework according to a set of relationships between regions. We also
define a new algorithm based on a pyramid of combinatorial maps which allows to
determine if one region contains the other using only local calculus.Comment: 35 page
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