19,287 research outputs found
Chain graph models of multivariate regression type for categorical data
We discuss a class of chain graph models for categorical variables defined by
what we call a multivariate regression chain graph Markov property. First, the
set of local independencies of these models is shown to be Markov equivalent to
those of a chain graph model recently defined in the literature. Next we
provide a parametrization based on a sequence of generalized linear models with
a multivariate logistic link function that captures all independence
constraints in any chain graph model of this kind.Comment: Published in at http://dx.doi.org/10.3150/10-BEJ300 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
The Quest for Optimal Sorting Networks: Efficient Generation of Two-Layer Prefixes
Previous work identifying depth-optimal -channel sorting networks for
is based on exploiting symmetries of the first two layers.
However, the naive generate-and-test approach typically applied does not scale.
This paper revisits the problem of generating two-layer prefixes modulo
symmetries. An improved notion of symmetry is provided and a novel technique
based on regular languages and graph isomorphism is shown to generate the set
of non-symmetric representations. An empirical evaluation demonstrates that the
new method outperforms the generate-and-test approach by orders of magnitude
and easily scales until
Bootstrap and the physical values of resonance parameters
This is the 6th paper in the series developing the formalism to manage the
effective scattering theory of strong interactions. Relying on the theoretical
scheme suggested in our previous publications we concentrate here on the
practical aspect and apply our technique to the elastic pion-nucleon scattering
amplitude. We test numerically the pion-nucleon spectrum sum rules that follow
from the tree level bootstrap constraints. We show how these constraints can be
used to estimate the tensor and vector coupling constants. At last, we
demonstrate that the tree-level low energy expansion coefficients computed in
the framework of our approach show nice agreement with known experimental data.
These results allow us to claim that the extended perturbation scheme is quite
reasonable from the computational point of view.Comment: 41 pages, 7 figure
Marginal log-linear parameters for graphical Markov models
Marginal log-linear (MLL) models provide a flexible approach to multivariate
discrete data. MLL parametrizations under linear constraints induce a wide
variety of models, including models defined by conditional independences. We
introduce a sub-class of MLL models which correspond to Acyclic Directed Mixed
Graphs (ADMGs) under the usual global Markov property. We characterize for
precisely which graphs the resulting parametrization is variation independent.
The MLL approach provides the first description of ADMG models in terms of a
minimal list of constraints. The parametrization is also easily adapted to
sparse modelling techniques, which we illustrate using several examples of real
data.Comment: 36 page
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