Decomposability of Multivariate Interactions

Decomposability of high-dimensional diversity measures: Quasi-U-statistics, martingales and nonstandard asymptotics

In complex diversity analysis, specially arising in genetics, genomics, ecology and other high-dimensional (and sometimes low sample size) data models, typically subgroup-decomposability (analogous to ANOVA decomposability) arises. In groupdivergence of diversity measures in a high-dimension low sample size scenario, it is shown that Hamming distance-type statistics lead to a general class of q...

Decomposability and selection of graphical models for multivariate time series

Complement of Special Chordal Graphs and Vertex Decomposability

In this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially Cohen-Macaulay.

Polynomial irreducibility testing through Minkowski summand computation

In this paper, we address the problem of deciding absolute irreducibility of multivariate polynomials. Our work has been motivated by a recent work due to Gao et. al. [1, 2, 3] where they have considered the problem for bivariate polynomials by studying the integral decomposability of polygons in the sense of Minkowski sum. We have generalized their result to polynomials containing arbitrary nu...

Exchangeable Hoeffding decompositions over finite sets: A combinatorial characterization and counterexamples

We study Hoeffding decomposable exchangeable sequences with values in a finite set D = {d1, . . . , dK}. We provide a new combinatorial characterization of Hoeffding decomposability and use this result to show that, for every K ≥ 3, there exists a class of neither Pólya nor i.i.d. D-valued exchangeable sequences that are Hoeffding decomposable.