Hierarchical Models for Independence Structures of Networks

We introduce a new family of network models, called hierarchical network models, that allow us to represent in an explicit manner the stochastic dependence among the dyads (random ties) of the network. In particular, each member of this family can be associated with a graphical model defining conditional independence clauses among the dyads of the network, called the dependency graph. Every network model with dyadic independence assumption can be generalized to construct members of this new family. Using this new framework, we generalize the Erd\"os-R\'enyi and beta-models to create hierarchical Erd\"os-R\'enyi and beta-models. We describe various methods for parameter estimation as well as simulation studies for models with sparse dependency graphs.Comment: 19 pages, 7 figure

On acceptance conditions for membrane systems: characterisations of L and NL

In this paper we investigate the affect of various acceptance conditions on recogniser membrane systems without dissolution. We demonstrate that two particular acceptance conditions (one easier to program, the other easier to prove correctness) both characterise the same complexity class, NL. We also find that by restricting the acceptance conditions we obtain a characterisation of L. We obtain these results by investigating the connectivity properties of dependency graphs that model membrane system computations

Nested Term Graphs (Work In Progress)

We report on work in progress on 'nested term graphs' for formalizing higher-order terms (e.g. finite or infinite lambda-terms), including those expressing recursion (e.g. terms in the lambda-calculus with letrec). The idea is to represent the nested scope structure of a higher-order term by a nested structure of term graphs. Based on a signature that is partitioned into atomic and nested function symbols, we define nested term graphs both in a functional representation, as tree-like recursive graph specifications that associate nested symbols with usual term graphs, and in a structural representation, as enriched term graph structures. These definitions induce corresponding notions of bisimulation between nested term graphs. Our main result states that nested term graphs can be implemented faithfully by first-order term graphs. keywords: higher-order term graphs, context-free grammars, cyclic lambda-terms, higher-order rewrite systemsComment: In Proceedings TERMGRAPH 2014, arXiv:1505.0681

Inference by Minimizing Size, Divergence, or their Sum

We speed up marginal inference by ignoring factors that do not significantly contribute to overall accuracy. In order to pick a suitable subset of factors to ignore, we propose three schemes: minimizing the number of model factors under a bound on the KL divergence between pruned and full models; minimizing the KL divergence under a bound on factor count; and minimizing the weighted sum of KL divergence and factor count. All three problems are solved using an approximation of the KL divergence than can be calculated in terms of marginals computed on a simple seed graph. Applied to synthetic image denoising and to three different types of NLP parsing models, this technique performs marginal inference up to 11 times faster than loopy BP, with graph sizes reduced up to 98%-at comparable error in marginals and parsing accuracy. We also show that minimizing the weighted sum of divergence and size is substantially faster than minimizing either of the other objectives based on the approximation to divergence presented here.Comment: Appears in Proceedings of the Twenty-Sixth Conference on Uncertainty in Artificial Intelligence (UAI2010