Related papers: Marginal Independence Models
Likelihood based-learning of graphical models faces challenges of computational-complexity and robustness to model mis-specification. This paper studies methods that fit parameters directly to maximize a measure of the accuracy of predicted…
We review a collection of models of random simplicial complexes together with some of the most exciting phenomena related to them. We do not attempt to cover all existing models, but try to focus on those for which many important results…
We develope the framework of transitional conditional independence. For this we introduce transition probability spaces and transitional random variables. These constructions will generalize, strengthen and unify previous notions of…
We consider a class of elliptic random matrices which generalize two classical ensembles from random matrix theory: Wigner matrices and random matrices with iid entries. In particular, we establish a central limit theorem for linear…
This chapter of the forthcoming Handbook of Graphical Models contains an overview of basic theorems and techniques from algebraic geometry and how they can be applied to the study of conditional independence and graphical models. It also…
We consider a generalization of an important class of high-dimensional inference problems, namely spiked symmetric matrix models, often used as probabilistic models for principal component analysis. Such paradigmatic models have recently…
We study random walks on contingency tables with fixed marginals, corresponding to a (log-linear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that are not connected.…
We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…
We study the small-regularisation limit of the entropic optimal transport problem on the line with distance cost. While convergence of entropic minimizers is well understood in the discrete setting and in the case where the cost is…
The edges of any hypergraph parametrize a monomial algebra called the edge subring of the hypergraph. We study presentation ideals of these edge subrings, and describe their generators in terms of balanced walks on hypergraphs. Our results…
We develop Markov categories as a framework for synthetic probability and statistics, following work of Golubtsov as well as Cho and Jacobs. This means that we treat the following concepts in purely abstract categorical terms: conditioning…
Statistical models of evolution are algebraic varieties in the space of joint probability distributions on the leaf colorations of a phylogenetic tree. The phylogenetic invariants of a model are the polynomials which vanish on the variety.…
We consider marginal log-linear models for parameterizing distributions on multidimensional contingency tables. These models generalize ordinary log-linear and multivariate logistic models, besides several others. First, we obtain some…
We study a marginal empirical likelihood approach in scenarios when the number of variables grows exponentially with the sample size. The marginal empirical likelihood ratios as functions of the parameters of interest are systematically…
For a class of integral operators with kernels metric functions on manifold we find some necessary and sufficient conditions to have finite rank. The problem we pose has a stochastic nature and boils down to the following alternative…
In many applications involving binary variables, only pairwise dependence measures, such as correlations, are available. However, for multi-way tables involving more than two variables, these quantities do not uniquely determine the joint…
For an arbitrary field K, let I be an ideal in the ring K[[x,y]] expressible as a polynomial in either the pair of ideals (x, y^4) and (x,y) or the pair (x,y^3) and (x^2, y). Let G be the group of automorphisms of K[[x,y]] sending the ideal…
In this lecture note, we discuss a fundamental concept, referred to as the {\it characteristic rank}, which suggests a general framework for characterizing the basic properties of various low-dimensional models used in signal processing.…
Extending the notion of indispensable binomials of a toric ideal, we define indispensable monomials of a toric ideal and establish some of their properties. They are useful for searching indispensable binomials of a toric ideal and for…
Single-index models or time-to-event models are frequently applied in empirical research. These models are non-identifiable in presence of unknown (dependent) censoring or competing risks and do not give informative results in empirical…