We formulate a novel approach to infer conditional independence models or Markov structure of a multivariate distribution. Specifically, our objective is to place informative prior distributions over decomposable graphs and sample efficiently from the induced posterior distribution. The key idea we develop in this paper is a parametrization of decomposable hypergraphs using the geometry of poin...

A univariate polynomial f over a field is decomposable if it is the composition f = g ◦h of two polynomials g and h whose degree is at least 2. We determine an approximation to the number of decomposable polynomials over a finite field. The tame case, where the field characteristic p does not divide the degree n of f , is reasonably well understood, and we obtain exponentially decreasing error ...

Entanglement in symmetric quantum states and the theory of copositive matrices are intimately related concepts. For simplest states, i.e., diagonal (DS) it has been shown that there exists a correspondence between exceptional (non-exceptional) non-decomposable (decomposable) Witnesses (EWs). Here we show EWs symmetric, but not DS, can also be constructed from extended matrices, providing new ex...

Consider a (possibly infinite) exchangeable sequence X= {Xn : 1≤ n < N}, where N ∈ N ∪ {∞}, with values in a Borel space (A,A), and note Xn = (X1, . . . ,Xn). We say that X is Hoeffding decomposable if, for each n, every square integrable, centered and symmetric statistic based on Xn can be written as an orthogonal sum of n U statistics with degenerated and symmetric kernels of increasing order...

In such areas as knowledge discovery, data mining and logical analysis of data, methodologies to 0nd relations among attributes are considered important. In this paper, given a data set (T; F) where T ⊆ {0; 1}n denotes a set of positive examples and F ⊆ {0; 1}n denotes a set of negative examples, we propose a method to identify decomposable structures among the attributes of the data. We 0rst s...

Let G be a finite group and A be a normal subgroup of G. We denote by ncc(A) the number of G-conjugacy classes of A and A is called n-decomposable, if ncc(A) = n. Set KG = {ncc(A)|A⊳ G}. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X . Ashrafi and his co-authors [1,2,3,4,5] have characterized the X-decomposable nonperfect finite groups for X = {1...