2,100 research outputs found
Lattices of Graphical Gaussian Models with Symmetries
In order to make graphical Gaussian models a viable modelling tool when the
number of variables outgrows the number of observations, model classes which
place equality restrictions on concentrations or partial correlations have
previously been introduced in the literature. The models can be represented by
vertex and edge coloured graphs. The need for model selection methods makes it
imperative to understand the structure of model classes. We identify four model
classes that form complete lattices of models with respect to model inclusion,
which qualifies them for an Edwards-Havr\'anek model selection procedure. Two
classes turn out most suitable for a corresponding model search. We obtain an
explicit search algorithm for one of them and provide a model search example
for the other.Comment: 29 pages, 18 figures. Restructured Section 5, results unchanged;
added references in Section 6; amended example in Section 6.
Estimation of means in graphical Gaussian models with symmetries
We study the problem of estimability of means in undirected graphical
Gaussian models with symmetry restrictions represented by a colored graph.
Following on from previous studies, we partition the variables into sets of
vertices whose corresponding means are restricted to being identical. We find a
necessary and sufficient condition on the partition to ensure equality between
the maximum likelihood and least-squares estimators of the mean.Comment: Published in at http://dx.doi.org/10.1214/12-AOS991 the Annals of
Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Linear Estimating Equations for Exponential Families with Application to Gaussian Linear Concentration Models
In many families of distributions, maximum likelihood estimation is
intractable because the normalization constant for the density which enters
into the likelihood function is not easily available. The score matching
estimator of Hyv\"arinen (2005) provides an alternative where this
normalization constant is not required. The corresponding estimating equations
become linear for an exponential family. The score matching estimator is shown
to be consistent and asymptotically normally distributed for such models,
although not necessarily efficient. Gaussian linear concentration models are
examples of such families. For linear concentration models that are also linear
in the covariance we show that the score matching estimator is identical to the
maximum likelihood estimator, hence in such cases it is also efficient.
Gaussian graphical models and graphical models with symmetries form
particularly interesting subclasses of linear concentration models and we
investigate the potential use of the score matching estimator for this case
A renormalization group computation of the critical exponents of hierarchical spin glasses
The infrared behaviour of a non-mean field spin-glass system is analysed, and
the critical exponent related to the divergence of the correlation length is
computed at two loops within the epsilon-expansion technique with two
independent methods. Both methods yield the same result confirming that the
infrared behaviour of the theory if well-defined and the underlying ideas of
the Renormalization Group hold also in such non-mean field disordered model. By
pushing such calculation to high orders in epsilon, a consistent and predictive
non-mean field theory for such disordered system could be established
Uniqueness of canonical tensor model with local time
Canonical formalism of the rank-three tensor model has recently been
proposed, in which "local" time is consistently incorporated by a set of first
class constraints. By brute-force analysis, this paper shows that there exist
only two forms of a Hamiltonian constraint which satisfies the following
assumptions: (i) A Hamiltonian constraint has one index. (ii) The kinematical
symmetry is given by an orthogonal group. (iii) A consistent first class
constraint algebra is formed by a Hamiltonian constraint and the generators of
the kinematical symmetry. (iv) A Hamiltonian constraint is invariant under time
reversal transformation. (v) A Hamiltonian constraint is an at most cubic
polynomial function of canonical variables. (vi) There are no disconnected
terms in a constraint algebra. The two forms are the same except for a slight
difference in index contractions. The Hamiltonian constraint which was obtained
in the previous paper and behaved oddly under time reversal symmetry can
actually be transformed to one of them by a canonical change of variables. The
two-fold uniqueness is shown up to the potential ambiguity of adding terms
which vanish in the limit of pure gravitational physics.Comment: 21 pages, 12 figures. The final result unchanged. Section 5 rewritten
for clearer discussions. The range of uniqueness commented in the final
section. Some other minor correction
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