8,126 research outputs found
Multilinear tensor regression for longitudinal relational data
A fundamental aspect of relational data, such as from a social network, is
the possibility of dependence among the relations. In particular, the relations
between members of one pair of nodes may have an effect on the relations
between members of another pair. This article develops a type of regression
model to estimate such effects in the context of longitudinal and multivariate
relational data, or other data that can be represented in the form of a tensor.
The model is based on a general multilinear tensor regression model, a special
case of which is a tensor autoregression model in which the tensor of relations
at one time point are parsimoniously regressed on relations from previous time
points. This is done via a separable, or Kronecker-structured, regression
parameter along with a separable covariance model. In the context of an
analysis of longitudinal multivariate relational data, it is shown how the
multilinear tensor regression model can represent patterns that often appear in
relational and network data, such as reciprocity and transitivity.Comment: Published at http://dx.doi.org/10.1214/15-AOAS839 in the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Modeling homophily and stochastic equivalence in symmetric relational data
This article discusses a latent variable model for inference and prediction
of symmetric relational data.
The model, based on the idea of the eigenvalue decomposition, represents the
relationship between two nodes as the weighted inner-product of node-specific
vectors of latent characteristics. This ``eigenmodel'' generalizes other
popular latent variable models, such as latent class and distance models: It is
shown mathematically that any latent class or distance model has a
representation as an eigenmodel, but not vice-versa. The practical implications
of this are examined in the context of three real datasets, for which the
eigenmodel has as good or better out-of-sample predictive performance than the
other two models.Comment: 12 pages, 4 figures, 1 tabl
Existence of global strong solutions in critical spaces for barotropic viscous fluids
This paper is dedicated to the study of viscous compressible barotropic
fluids in dimension . We address the question of the global existence
of strong solutions for initial data close from a constant state having
critical Besov regularity. In a first time, this article show the recent
results of \cite{CD} and \cite{CMZ} with a new proof. Our result relies on a
new a priori estimate for the velocity, where we introduce a new structure to
\textit{kill} the coupling between the density and the velocity as in
\cite{H2}. We study so a new variable that we call effective velocity. In a
second time we improve the results of \cite{CD} and \cite{CMZ} by adding some
regularity on the initial data in particular is in . In this
case we obtain global strong solutions for a class of large initial data on the
density and the velocity which in particular improve the results of D. Hoff in
\cite{5H4}. We conclude by generalizing these results for general viscosity
coefficients
- …