Refining a Bayesian network using a chain event graph

The search for a useful explanatory model based on a Bayesian Network (BN) now has a long and successful history. However, when the dependence structure between the variables of the problem is asymmetric then this cannot be captured by the BN. The Chain Event Graph (CEG) provides a richer class of models which incorporates these types of dependence structures as well as retaining the property that conclusions can be easily read back to the client. We demonstrate on a real health study how the CEG leads us to promising higher scoring models and further enables us to make more refined conclusions than can be made from the BN. Further we show how these graphs can express causal hypotheses about possible interventions that could be enforced

Equivalence Classes of Staged Trees

In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then, simple transformations on that polynomial enable us to traverse the corresponding class of graphs. We illustrate our results with a real analysis of the implicit dependence relationships within a previously studied dataset.Comment: 18 pages, 4 figure

Augmenting citation chain aggregation with article maps

Presentation slides available at: https://www.gesis.org/fileadmin/upload/kmir2014/paper4_slides.pdfThis paper presents Voyster, an experimental system that combines citation chain aggregation (CCA) and spatial-semantic maps to support citation search. CCA uses a three-list view to represent the citation network surrounding a ‘pearl’ of known relevant articles, whereby cited and citing articles are ranked according to number of pearl relations. As the pearl grows, this overlap score provides an effective proxy for relevance. However, when the pearl is small or multi-faceted overlap ranking provides poor discrimination. To address this problem we augment the lists with a visual map, wherein articles are organized according to their content similarity. We demonstrate how the article map can help the user to make relevant choices during the early stages of the search pro-cess and also provide useful insights into the thematic structure of the local citation network

Equations defining probability tree models

Coloured probability tree models are statistical models coding conditional independence between events depicted in a tree graph. They are more general than the very important class of context-specific Bayesian networks. In this paper, we study the algebraic properties of their ideal of model invariants. The generators of this ideal can be easily read from the tree graph and have a straightforward interpretation in terms of the underlying model: they are differences of odds ratios coming from conditional probabilities. One of the key findings in this analysis is that the tree is a convenient tool for understanding the exact algebraic way in which the sum-to-1 conditions on the parameter space translate into the sum-to-one conditions on the joint probabilities of the statistical model. This enables us to identify necessary and sufficient graphical conditions for a staged tree model to be a toric variety intersected with a probability simplex.Comment: 22 pages, 4 figure

Using Space Syntax For Estimation Of Potential Disaster Indirect Economic Losses

The study of applicable network measures shows that Normalised Angular Choice can be used as criteria for selecting alternatives for minimizing indirect costs caused by road network damages. At the same time, this methodology cannot be used for monetizing indirect costs or identifying losses in different economic sectors. The study approach does not contradict the main theoretical approaches and it gives new opportunities for research on disasters recovery

The Power Light Cone of the Discrete Bak-Sneppen, Contact and other local processes

We consider a class of random processes on graphs that include the discrete Bak-Sneppen (DBS) process and the several versions of the contact process (CP), with a focus on the former. These processes are parametrized by a probability $0\leq p \leq 1$ that controls a local update rule. Numerical simulations reveal a phase transition when $p$ goes from 0 to 1. Analytically little is known about the phase transition threshold, even for one-dimensional chains. In this article we consider a power-series approach based on representing certain quantities, such as the survival probability or the expected number of steps per site to reach the steady state, as a power-series in $p$. We prove that the coefficients of those power series stabilize as the length $n$ of the chain grows. This is a phenomenon that has been used in the physics community but was not yet proven. We show that for local events $A,B$ of which the support is a distance $d$ apart we have $\mathrm{cor}(A,B) = \mathcal{O}(p^d)$. The stabilization allows for the (exact) computation of coefficients for arbitrary large systems which can then be analyzed using the wide range of existing methods of power series analysis.Comment: 25 pages, 5 figure