In this paper, we introduce a class of a directed acyclic graph on the assumption that the collection of random variables indexed by the vertices has a Markov property. We present a flexible approach for the study of the exact distributions of runs and scans on the directed acyclic graph by...

Random Forests in combination with Stability Selection allow to estimate stable conditional independence graphs with an error control mechanism for false positive selection. This approach is applicable to graphs containing both continuous and discrete variables at the same time. Its performance...

We present a framework for sequential decision making in problems described by graphical models. The setting is given by dependent discrete random variables with associated costs or revenues. In our examples, the dependent variables are the potential outcomes (oil, gas or dry) when drilling a...

Motivated by analysis of gene expression data measured over different tissues or over time, we consider matrix-valued random variable and matrix-normal distribution, where the precision matrices have a graphical interpretation for genes and tissues, respectively. We present a l1 penalized...

In many applications of graphical models arising in computer vision, the hidden variables of interest are most naturally specified by continuous, non-Gaussian distributions. There exist inference algorithms for discrete approximations to these continuous distributions, but for the...