268,601 research outputs found
Spectral Estimation of Conditional Random Graph Models for Large-Scale Network Data
Generative models for graphs have been typically committed to strong prior
assumptions concerning the form of the modeled distributions. Moreover, the
vast majority of currently available models are either only suitable for
characterizing some particular network properties (such as degree distribution
or clustering coefficient), or they are aimed at estimating joint probability
distributions, which is often intractable in large-scale networks. In this
paper, we first propose a novel network statistic, based on the Laplacian
spectrum of graphs, which allows to dispense with any parametric assumption
concerning the modeled network properties. Second, we use the defined statistic
to develop the Fiedler random graph model, switching the focus from the
estimation of joint probability distributions to a more tractable conditional
estimation setting. After analyzing the dependence structure characterizing
Fiedler random graphs, we evaluate them experimentally in edge prediction over
several real-world networks, showing that they allow to reach a much higher
prediction accuracy than various alternative statistical models.Comment: Appears in Proceedings of the Twenty-Eighth Conference on Uncertainty
in Artificial Intelligence (UAI2012
Local Statistical Modeling via Cluster-Weighted Approach with Elliptical Distributions
Cluster Weighted Modeling (CWM) is a mixture approach regarding the modelisation of the joint probability of data coming from a heterogeneous population. Under Gaussian assumptions, we investigate statistical properties of CWM from both the theoretical and numerical point of view; in particular, we show that CWM includes as special cases mixtures of distributions and mixtures of regressions. Further, we introduce CWM based on Student-t distributions providing more robust fitting for groups of observations with longer than normal tails or atypical observations. Theoretical results are illustrated using some empirical studies, considering both real and simulated data.Cluster-Weighted Modeling, Mixture Models, Model-Based Clustering
Qubit-portraits of qudit states and quantum correlations
The machinery of qubit-portraits of qudit states, recently presented, is
consider here in more details in order to characterize the presence of quantum
correlations in bipartite qudit states. In the tomographic representation of
quantum mechanics, Bell-like inequalities are interpreted as peculiar
properties of a family of classical joint probability distributions which
describe the quantum state of two qudits. By means of the qubit-portraits
machinery a semigroup of stochastic matrices can be associated to a given
quantum state. The violation of the CHSH inequalities is discussed in this
framework with some examples, we found that quantum correlations in qutrit
isotropic states can be detected by the suggested method while it cannot in the
case of qutrit Werner states.Comment: 12 pages, 4 figure
Spin glass models from the point of view of spin distributions
In many spin glass models, due to the symmetry among sites, any limiting
joint distribution of spins under the annealed Gibbs measure admits the
Aldous-Hoover representation encoded by a function
, and one can think of this function as a generic
functional order parameter of the model. In a class of diluted models, and in
the Sherrington-Kirkpatrick model, we introduce novel perturbations of the
Hamiltonian that yield certain invariance and self-consistency equations for
this generic functional order parameter and we use these invariance properties
to obtain representations for the free energy in terms of . In the
setting of the Sherrington-Kirkpatrick model, the self-consistency equations
imply that the joint distribution of spins is determined by the joint
distributions of the overlaps, and we give an explicit formula for
under the Parisi ultrametricity hypothesis. In addition, we discuss some
connections with the Ghirlanda-Guerra identities and stochastic stability and
describe the expected Parisi ansatz in the diluted models in terms of .Comment: Published in at http://dx.doi.org/10.1214/11-AOP696 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
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