2,637 research outputs found
Learning Markov Structure by Maximum Entropy Relaxation
We propose a new approach for learning
a sparse graphical model approximation to
a specified multivariate probability distribution
(such as the empirical distribution
of sample data). The selection of sparse
graph structure arises naturally in our approach
through solution of a convex optimization
problem, which differentiates our
method from standard combinatorial approaches.
We seek the maximum entropy relaxation
(MER) within an exponential family,
which maximizes entropy subject to constraints
that marginal distributions on small
subsets of variables are close to the prescribed
marginals in relative entropy. To solve MER,
we present a modified primal-dual interior
point method that exploits sparsity of the
Fisher information matrix in models defined
on chordal graphs. This leads to a tractable,
scalable approach provided the level of relaxation
in MER is sufficient to obtain a thin
graph. The merits of our approach are investigated
by recovering the structure of some
simple graphical models from sample data
Networking - A Statistical Physics Perspective
Efficient networking has a substantial economic and societal impact in a
broad range of areas including transportation systems, wired and wireless
communications and a range of Internet applications. As transportation and
communication networks become increasingly more complex, the ever increasing
demand for congestion control, higher traffic capacity, quality of service,
robustness and reduced energy consumption require new tools and methods to meet
these conflicting requirements. The new methodology should serve for gaining
better understanding of the properties of networking systems at the macroscopic
level, as well as for the development of new principled optimization and
management algorithms at the microscopic level. Methods of statistical physics
seem best placed to provide new approaches as they have been developed
specifically to deal with non-linear large scale systems. This paper aims at
presenting an overview of tools and methods that have been developed within the
statistical physics community and that can be readily applied to address the
emerging problems in networking. These include diffusion processes, methods
from disordered systems and polymer physics, probabilistic inference, which
have direct relevance to network routing, file and frequency distribution, the
exploration of network structures and vulnerability, and various other
practical networking applications.Comment: (Review article) 71 pages, 14 figure
Approximating the Permanent with Fractional Belief Propagation
We discuss schemes for exact and approximate computations of permanents, and
compare them with each other. Specifically, we analyze the Belief Propagation
(BP) approach and its Fractional Belief Propagation (FBP) generalization for
computing the permanent of a non-negative matrix. Known bounds and conjectures
are verified in experiments, and some new theoretical relations, bounds and
conjectures are proposed. The Fractional Free Energy (FFE) functional is
parameterized by a scalar parameter , where
corresponds to the BP limit and corresponds to the exclusion
principle (but ignoring perfect matching constraints) Mean-Field (MF) limit.
FFE shows monotonicity and continuity with respect to . For every
non-negative matrix, we define its special value to be the
for which the minimum of the -parameterized FFE functional is
equal to the permanent of the matrix, where the lower and upper bounds of the
-interval corresponds to respective bounds for the permanent. Our
experimental analysis suggests that the distribution of varies for
different ensembles but always lies within the interval.
Moreover, for all ensembles considered the behavior of is highly
distinctive, offering an emprirical practical guidance for estimating
permanents of non-negative matrices via the FFE approach.Comment: 42 pages, 14 figure
Approximate inference techniques with expectation constraints
Contains fulltext :
100937.pdf (preprint version ) (Open Access
- …