873 research outputs found
Generalized Permutohedra from Probabilistic Graphical Models
A graphical model encodes conditional independence relations via the Markov
properties. For an undirected graph these conditional independence relations
can be represented by a simple polytope known as the graph associahedron, which
can be constructed as a Minkowski sum of standard simplices. There is an
analogous polytope for conditional independence relations coming from a regular
Gaussian model, and it can be defined using multiinformation or relative
entropy. For directed acyclic graphical models and also for mixed graphical
models containing undirected, directed and bidirected edges, we give a
construction of this polytope, up to equivalence of normal fans, as a Minkowski
sum of matroid polytopes. Finally, we apply this geometric insight to construct
a new ordering-based search algorithm for causal inference via directed acyclic
graphical models.Comment: Appendix B is expanded. Final version to appear in SIAM J. Discrete
Mat
Multisite Weather Generators Using Bayesian Networks: An Illustrative Case Study for Precipitation Occurrence
ABSTRACT: Many existing approaches for multisite weather generation try to capture several statistics of the observed data (e.g. pairwise correlations) in order to generate spatially and temporarily consistent series. In this work we analyse the application of Bayesian networks to this problem, focusing on precipitation occurrence and considering a simple case study to illustrate the potential of this new approach. We use Bayesian networks to approximate the multi-variate (-site) probability distribution of observed gauge data, which is factorized according to the relevant (marginal and conditional) dependencies. This factorization allows the simulation of synthetic samples from the multivariate distribution, thus providing a sound and promising methodology for multisite precipitation series generation.We acknowledge funding provided by the project MULTI‐SDM (CGL2015‐ 66583‐R, MINECO/FEDER)
The IBMAP approach for Markov networks structure learning
In this work we consider the problem of learning the structure of Markov
networks from data. We present an approach for tackling this problem called
IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC
algorithm, designed for avoiding important limitations of existing
independence-based algorithms. These algorithms proceed by performing
statistical independence tests on data, trusting completely the outcome of each
test. In practice tests may be incorrect, resulting in potential cascading
errors and the consequent reduction in the quality of the structures learned.
IBMAP contemplates this uncertainty in the outcome of the tests through a
probabilistic maximum-a-posteriori approach. The approach is instantiated in
the IBMAP-HC algorithm, a structure selection strategy that performs a
polynomial heuristic local search in the space of possible structures. We
present an extensive empirical evaluation on synthetic and real data, showing
that our algorithm outperforms significantly the current independence-based
algorithms, in terms of data efficiency and quality of learned structures, with
equivalent computational complexities. We also show the performance of IBMAP-HC
in a real-world application of knowledge discovery: EDAs, which are
evolutionary algorithms that use structure learning on each generation for
modeling the distribution of populations. The experiments show that when
IBMAP-HC is used to learn the structure, EDAs improve the convergence to the
optimum
Current-induced cooling phenomenon in a two-dimensional electron gas under a magnetic field
We investigate the spatial distribution of temperature induced by a dc
current in a two-dimensional electron gas (2DEG) subjected to a perpendicular
magnetic field. We numerically calculate the distributions of the electrostatic
potential phi and the temperature T in a 2DEG enclosed in a square area
surrounded by insulated-adiabatic (top and bottom) and isopotential-isothermal
(left and right) boundaries (with phi_{left} < phi_{right} and T_{left}
=T_{right}), using a pair of nonlinear Poisson equations (for phi and T) that
fully take into account thermoelectric and thermomagnetic phenomena, including
the Hall, Nernst, Ettingshausen, and Righi-Leduc effects. We find that, in the
vicinity of the left-bottom corner, the temperature becomes lower than the
fixed boundary temperature, contrary to the naive expectation that the
temperature is raised by the prevalent Joule heating effect. The cooling is
attributed to the Ettingshausen effect at the bottom adiabatic boundary, which
pumps up the heat away from the bottom boundary. In order to keep the adiabatic
condition, downward temperature gradient, hence the cooled area, is developed
near the boundary, with the resulting thermal diffusion compensating the upward
heat current due to the Ettingshausen effect.Comment: 25 pages, 7 figure
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HVEM quantitative stereoscopy through the full damage range of an ion- bombarded Fe--Ni--Cr alloy
The swelling of a Ni-ion irradiated Fe--25 percent Ni--15 percent Cr alloy has been investigated employing high voltage (1 MeV) electron microscopy. Helium pre-injected samples were irradiated to a maximum dose of 92 dpa with 3.5 MeV Ni ions at 600, 650, 700 and 750C. By means of quantitative stereoscopy throughout the full range of ion damage, the void morphology, swelling, and dislocation morphology as functions of the distance from the ion-entry surface of the foil were obtained. The dose also varied as a function of depth and, with this technique, swelling as a function of dose was determined from a single sample at each temperature. Swelling, void concentration, and void size varied with irradiation temperature with the maximum swelling of 7.4 percent occurring at 700C. Several distinct dislocation configurations could be distinguished progressing inward from the ion-entry surface. The observations suggest that nucleation and growth of voids are related to dislocation densities and possibly to dislocation structure. The swelling-dose relationships were analyzed using a linear expression for each apparent swelling regime and the results interpreted in terms of the Brailsford and Bullough statistical rate theory. Two distinct steady-state swelling regimes exist at each irradiation temperature and the difference in the rates is attributed to the different kinetic development of the dislocation structure and densities in the two stages. (auth
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Approximating the Shapley Value via Multi-Issue Decomposition
The Shapley value provides a fair method for the division of value in coalitional games. Motivated by the application of crowdsourcing for the collection of suitable labels and features for regression and classification tasks, we develop a method to approximate the Shapley value by identifying a suitable decomposition into multiple issues, with the decomposition computed by applying a graph partitioning to a pairwise similarity graph induced by the coalitional value function. The method is significantly faster and more accurate than existing random-sampling based methods on both synthetic data and data representing user contributions in a real world application of crowdsourcing to elicit labels and features for classification.Engineering and Applied Science
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