23,736 research outputs found
Multilevel coarse graining and nano--pattern discovery in many particle stochastic systems
In this work we propose a hierarchy of Monte Carlo methods for sampling
equilibrium properties of stochastic lattice systems with competing short and
long range interactions. Each Monte Carlo step is composed by two or more sub -
steps efficiently coupling coarse and microscopic state spaces. The method can
be designed to sample the exact or controlled-error approximations of the
target distribution, providing information on levels of different resolutions,
as well as at the microscopic level. In both strategies the method achieves
significant reduction of the computational cost compared to conventional Markov
Chain Monte Carlo methods. Applications in phase transition and pattern
formation problems confirm the efficiency of the proposed methods.Comment: 37 page
Infinite factorization of multiple non-parametric views
Combined analysis of multiple data sources has increasing application interest, in particular for distinguishing shared and source-specific aspects. We extend this rationale of classical canonical correlation analysis into a flexible, generative and non-parametric clustering
setting, by introducing a novel non-parametric hierarchical
mixture model. The lower level of the model describes each source with a flexible non-parametric mixture, and the top level combines these to describe commonalities of the sources. The lower-level clusters arise from hierarchical Dirichlet Processes, inducing an infinite-dimensional contingency table between the views. The commonalities between the sources are modeled by an infinite block
model of the contingency table, interpretable as non-negative factorization of infinite matrices, or as a prior for infinite contingency tables. With Gaussian mixture components plugged in for continuous measurements, the model is applied to two views of genes, mRNA expression and abundance of the produced proteins, to expose groups of genes that are co-regulated in either or both of the views.
Cluster analysis of co-expression is a standard simple way of screening for co-regulation, and the two-view analysis extends the approach to distinguishing between pre- and post-translational regulation
On Measure Concentration of Random Maximum A-Posteriori Perturbations
The maximum a-posteriori (MAP) perturbation framework has emerged as a useful
approach for inference and learning in high dimensional complex models. By
maximizing a randomly perturbed potential function, MAP perturbations generate
unbiased samples from the Gibbs distribution. Unfortunately, the computational
cost of generating so many high-dimensional random variables can be
prohibitive. More efficient algorithms use sequential sampling strategies based
on the expected value of low dimensional MAP perturbations. This paper develops
new measure concentration inequalities that bound the number of samples needed
to estimate such expected values. Applying the general result to MAP
perturbations can yield a more efficient algorithm to approximate sampling from
the Gibbs distribution. The measure concentration result is of general interest
and may be applicable to other areas involving expected estimations
Extremal decomposition for random Gibbs measures: From general metastates to metastates on extremal random Gibbs measures
The concept of metastate measures on the states of a random spin system was
introduced to be able to treat the large-volume asymptotics for complex
quenched random systems, like spin glasses, which may exhibit chaotic volume
dependence in the strong-coupling regime. We consider the general issue of the
extremal decomposition for Gibbsian specifications which depend measurably on a
parameter that may describe a whole random environment in the infinite volume.
Given a random Gibbs measure, as a measurable map from the environment space,
we prove measurability of its decomposition measure on pure states at fixed
environment, with respect to the environment. As a general corollary we obtain
that, for any metastate, there is an associated decomposition metastate, which
is supported on the extremes for almost all environments, and which has the
same barycenter.Comment: 12 page
Sufficient conditions for convergence of the Sum-Product Algorithm
We derive novel conditions that guarantee convergence of the Sum-Product
algorithm (also known as Loopy Belief Propagation or simply Belief Propagation)
to a unique fixed point, irrespective of the initial messages. The
computational complexity of the conditions is polynomial in the number of
variables. In contrast with previously existing conditions, our results are
directly applicable to arbitrary factor graphs (with discrete variables) and
are shown to be valid also in the case of factors containing zeros, under some
additional conditions. We compare our bounds with existing ones, numerically
and, if possible, analytically. For binary variables with pairwise
interactions, we derive sufficient conditions that take into account local
evidence (i.e., single variable factors) and the type of pair interactions
(attractive or repulsive). It is shown empirically that this bound outperforms
existing bounds.Comment: 15 pages, 5 figures. Major changes and new results in this revised
version. Submitted to IEEE Transactions on Information Theor
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