Related papers: Conditional Independence in Max-linear Bayesian Ne…

We propose two types of Quantile Graphical Models (QGMs) --- Conditional Independence Quantile Graphical Models (CIQGMs) and Prediction Quantile Graphical Models (PQGMs). CIQGMs characterize the conditional independence of distributions by…

We extend the notions of conditioned and controlled invariant spaces to linear dynamical systems over the max-plus or tropical semiring. We establish a duality theorem relating both notions, which we use to construct dynamic observers.…

This study presents a dynamic Bayesian network framework that facilitates intuitive gradual edge changes. We use two conditional dynamics to model the edge addition and deletion, and edge selection separately. Unlike previous research that…

A structural equation model (SEM) is an effective framework to reason over causal relationships represented via a directed acyclic graph (DAG). Recent advances have enabled effective maximum-likelihood point estimation of DAGs from…

Heckerman (1993) defined causal independence in terms of a set of temporal conditional independence statements. These statements formalized certain types of causal interaction where (1) the effect is independent of the order that causes are…

We give a sufficient condition for an algebraic structure to have a computable presentation with a computable basis and a computable presentation with no computable basis. We apply the condition to differentially closed, real closed, and…

Learning causal relations from observational data is a fundamental problem with wide-ranging applications across many fields. Constraint-based methods infer the underlying causal structure by performing conditional independence tests.…

Theory of graphical models has matured over more than three decades to provide the backbone for several classes of models that are used in a myriad of applications such as genetic mapping of diseases, credit risk evaluation, reliability and…

This paper considers the problem of defining distributions over graphical structures. We propose an extension of the hyper Markov properties of Dawid and Lauritzen [Ann. Statist. 21 (1993) 1272-1317], which we term structural Markov…

In this work, dynamic Bayesian multinets are introduced where a Markov chain state at time t determines conditional independence patterns between random variables lying within a local time window surrounding t. It is shown how…

This work investigates the intersection property of conditional independence. It states that for random variables $A,B,C$ and $X$ we have that $X$ independent of $A$ given $B,C$ and $X$ independent of $B$ given $A,C$ implies $X$ independent…

Pearls concept OF a d - connecting path IS one OF the foundations OF the modern theory OF graphical models : the absence OF a d - connecting path IN a DAG indicates that conditional independence will hold IN ANY distribution factorising…

We consider the problem of inferring the conditional independence graph (CIG) of a multivariate stationary dicrete-time Gaussian random process based on a finite length observation. Using information-theoretic methods, we derive a lower…

Extreme value statistics is the max analogue of classical statistics, while tropical geometry is the max analogue of classical geometry. In this paper, we review recent work where insights from tropical geometry were used to develop new,…

Multivariate extreme value analysis quantifies the probability and magnitude of joint extreme events. River discharges from the upper Danube River basin provide a challenging dataset for such analysis because the data, which is measured on…

A Bayesian Network is a directed acyclic graph (DAG) on a set of $n$ random variables (the vertices); a Bayesian Network Distribution (BND) is a probability distribution on the random variables that is Markovian on the graph. A finite…

This paper presents a Bayesian inference framework for a linear index threshold-crossing binary choice model that satisfies a median independence restriction. The key idea is that the model is observationally equivalent to a probit model…

While logistic regression models are easily accessible to researchers, when applied to network data there are unrealistic assumptions made about the dependence structure of the data. For temporal networks measured in discrete time, recent…

A variety of statistical graphical models have been defined to represent the conditional independences underlying a random vector of interest. Similarly, many different graphs embedding various types of preferential independences, as for…

Conditioned limit laws constitute an important and well developed framework of extreme value theory that describe a broad range of extremal dependence forms including asymptotic independence. We explore the assumption of conditional…