Taming Graphical Modeling

Visual models help to understand complex systems. However, with the user interaction paradigms established today, activities such as creating, maintaining or browsing visual models can be very tedious. Valuable engineering time is wasted with archaic activities such as manual placement and routing of nodes and edges. This report presents an approach to enhance productivity by focusing on the pragmatics of model-based design. Our contribution is twofold: First, the concept of meta layout enables the synthesis of different diagrammatic views on graphical models. This modularly employs sophisticated layout algorithms, closing the gap between MDE and graph drawing theory. Second, a view management logic harnesses this auto layout to present customized views on models. These concepts have been implemented in the open source Kiel Integrated Environment for Layout Eclipse Rich Client (KIELER). Two applications---editing and simulation---illustrate how view management helps to increase developer productivity and tame model complexity

GMF: A Model Migration Case for the Transformation Tool Contest

Using a real-life evolution taken from the Graphical Modeling Framework, we invite submissions to explore ways in which model transformation and migration tools can be used to migrate models in response to metamodel adaptation.Comment: In Proceedings TTC 2011, arXiv:1111.440

Graphical modeling of stochastic processes driven by correlated errors

We study a class of graphs that represent local independence structures in stochastic processes allowing for correlated error processes. Several graphs may encode the same local independencies and we characterize such equivalence classes of graphs. In the worst case, the number of conditions in our characterizations grows superpolynomially as a function of the size of the node set in the graph. We show that deciding Markov equivalence is coNP-complete which suggests that our characterizations cannot be improved upon substantially. We prove a global Markov property in the case of a multivariate Ornstein-Uhlenbeck process which is driven by correlated Brownian motions.Comment: 43 page

One-Component Regular Variation and Graphical Modeling of Extremes

The problem of inferring the distribution of a random vector given that its norm is large requires modeling a homogeneous limiting density. We suggest an approach based on graphical models which is suitable for high-dimensional vectors. We introduce the notion of one-component regular variation to describe a function that is regularly varying in its first component. We extend the representation and Karamata's theorem to one-component regularly varying functions, probability distributions and densities, and explain why these results are fundamental in multivariate extreme-value theory. We then generalize Hammersley-Clifford theorem to relate asymptotic conditional independence to a factorization of the limiting density, and use it to model multivariate tails

Graphical Modeling for Multivariate Hawkes Processes with Nonparametric Link Functions

Hawkes (1971) introduced a powerful multivariate point process model of mutually exciting processes to explain causal structure in data. In this paper it is shown that the Granger causality structure of such processes is fully encoded in the corresponding link functions of the model. A new nonparametric estimator of the link functions based on a time-discretized version of the point process is introduced by using an infinite order autoregression. Consistency of the new estimator is derived. The estimator is applied to simulated data and to neural spike train data from the spinal dorsal horn of a rat.Comment: 20 pages, 4 figure