Markov approximation of arbitrary random field on homogeneous trees
نویسندگان
چکیده
* Correspondence: [email protected] Department of Mathematics, Chaohu University Chaohu, 238000, P.R. China Full list of author information is available at the end of the article Abstract In this article, we establish a class of small deviation theorems for functionals of random fields and the strong law of large numbers for the ordered couple of states for arbitrary random fields on homogenous trees. A known result is generalized in this article. 2010 Mathematics Subject Classification: 60J10; 60F15.
منابع مشابه
Consistent Markov branching trees with discrete edge lengths∗
We study consistent collections of random fragmentation trees with random integervalued edge lengths. We prove several equivalent necessary and sufficient conditions under which Geometrically distributed edge lengths can be consistently assigned to a Markov branching tree. Among these conditions is a characterization by a unique probability measure, which plays a role similar to the dislocation...
متن کاملSubset Selection for Gaussian Markov Random Fields
Given a Gaussian Markov random field, we consider the problem of selecting a subset of variables to observe which minimizes the total expected squared prediction error of the unobserved variables. We first show that finding an exact solution is NP-hard even for a restricted class of Gaussian Markov random fields, called Gaussian free fields, which arise in semi-supervised learning and computer ...
متن کاملAccuracy of Discrete Markov Approximation in the Problems of Estimation of Random Field Characteristics
The covariance matrix of measurements of Markov random fields (processes) has useful properties that allow to develop effective computational algorithms for many problems in the study of Markov fields on the basis of field observations (parametric identification problems, filtering problems, interpolation problems and others). Therefore, approximation of arbitrary random fields by Markov fields...
متن کاملNegative Tree Reweighted Belief Propagation
We introduce a new class of lower bounds on the log partition function of a Markov random field which makes use of a reversed Jensen’s inequality. In particular, our method approximates the intractable distribution using a linear combination of spanning trees with negative weights. This technique is a lower-bound counterpart to the tree-reweighted belief propagation algorithm, which uses a conv...
متن کاملVariance on the Leaves of a Tree Markov Random Field: Detecting Character Dependencies in Phylogenies
Stochastic models of evolution (Markov random fields on trivalent trees) generally assume that different characters (different runs of the stochastic process) are independent and identically distributed. In this paper we take the first steps towards addressing dependent characters. Specifically we show that, under certain technical assumptions regarding the evolution of individual characters, w...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012