5,355 research outputs found
Stochastic Weighted Graphs: Flexible Model Specification and Simulation
In most domains of network analysis researchers consider networks that arise
in nature with weighted edges. Such networks are routinely dichotomized in the
interest of using available methods for statistical inference with networks.
The generalized exponential random graph model (GERGM) is a recently proposed
method used to simulate and model the edges of a weighted graph. The GERGM
specifies a joint distribution for an exponential family of graphs with
continuous-valued edge weights. However, current estimation algorithms for the
GERGM only allow inference on a restricted family of model specifications. To
address this issue, we develop a Metropolis--Hastings method that can be used
to estimate any GERGM specification, thereby significantly extending the family
of weighted graphs that can be modeled with the GERGM. We show that new
flexible model specifications are capable of avoiding likelihood degeneracy and
efficiently capturing network structure in applications where such models were
not previously available. We demonstrate the utility of this new class of
GERGMs through application to two real network data sets, and we further assess
the effectiveness of our proposed methodology by simulating non-degenerate
model specifications from the well-studied two-stars model. A working R version
of the GERGM code is available in the supplement and will be incorporated in
the gergm CRAN package.Comment: 33 pages, 6 figures. To appear in Social Network
Endoscopic transfer of orbital integrals in large residual characteristic
This article constructs Shalika germs in the context of motivic integration,
both for ordinary orbital integrals and kappa-orbital integrals. Based on
transfer principles in motivic integration and on Waldspurger's endoscopic
transfer of smooth functions in characteristic zero, we deduce the endoscopic
transfer of smooth functions in sufficiently large residual characteristic.Comment: 33 page
Group Symmetry and non-Gaussian Covariance Estimation
We consider robust covariance estimation with group symmetry constraints.
Non-Gaussian covariance estimation, e.g., Tyler scatter estimator and
Multivariate Generalized Gaussian distribution methods, usually involve
non-convex minimization problems. Recently, it was shown that the underlying
principle behind their success is an extended form of convexity over the
geodesics in the manifold of positive definite matrices. A modern approach to
improve estimation accuracy is to exploit prior knowledge via additional
constraints, e.g., restricting the attention to specific classes of covariances
which adhere to prior symmetry structures. In this paper, we prove that such
group symmetry constraints are also geodesically convex and can therefore be
incorporated into various non-Gaussian covariance estimators. Practical
examples of such sets include: circulant, persymmetric and complex/quaternion
proper structures. We provide a simple numerical technique for finding maximum
likelihood estimates under such constraints, and demonstrate their performance
advantage using synthetic experiments
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