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...

We consider the problem of learning Bayesian networks optimally, when subject to background knowledge in the form of ancestral constraints. Our approach is based on a recently proposed framework for optimal structure learning based on non-decomposable scores, which is general enough to accommodate ancestral constraints. The proposed framework exploits oracles for learning structures using decom...

In symmetric tensor decomposition one expresses a given symmetric tensor T a sum of tensor powers of a number of vectors: T = v⊗d 1 + · · · + v ⊗d k . Orthogonal decomposition is a special type of symmetric tensor decomposition in which in addition the vectors v1, ..., vk are required to be pairwise orthogonal. We study the properties of orthogonally decomposable tensors. In particular, we give...

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 ...

We consider the dihamiltonian decomposition problem for 3regular graphs. A graphG is dihamiltonian decomposable if in the digraph obtained fromG by replacing each edge of G as two directed edges, the set of edges are partitioned into 3 edge-disjoint directed hamiltonian cycles. We suggest some conditions for dihamiltonian decomposition of 3-regular graphs: for a 3-regular graph G, it is dihamil...