Efficient Localized Inference for Large Graphical Models

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models

Topology Discovery of Sparse Random Graphs With Few Participants

We consider the task of topology discovery of sparse random graphs using end-to-end random measurements (e.g., delay) between a subset of nodes, referred to as the participants. The rest of the nodes are hidden, and do not provide any information for topology discovery. We consider topology discovery under two routing models: (a) the participants exchange messages along the shortest paths and obtain end-to-end measurements, and (b) additionally, the participants exchange messages along the second shortest path. For scenario (a), our proposed algorithm results in a sub-linear edit-distance guarantee using a sub-linear number of uniformly selected participants. For scenario (b), we obtain a much stronger result, and show that we can achieve consistent reconstruction when a sub-linear number of uniformly selected nodes participate. This implies that accurate discovery of sparse random graphs is tractable using an extremely small number of participants. We finally obtain a lower bound on the number of participants required by any algorithm to reconstruct the original random graph up to a given edit distance. We also demonstrate that while consistent discovery is tractable for sparse random graphs using a small number of participants, in general, there are graphs which cannot be discovered by any algorithm even with a significant number of participants, and with the availability of end-to-end information along all the paths between the participants.Comment: A shorter version appears in ACM SIGMETRICS 2011. This version is scheduled to appear in J. on Random Structures and Algorithm

Multi-Paradigm Reasoning for Access to Heterogeneous GIS

Accessing and querying geographical data in a uniform way has become easier in recent years. Emerging standards like WFS turn the web into a geospatial web services enabled place. Mediation architectures like VirGIS overcome syntactical and semantical heterogeneity between several distributed sources. On mobile devices, however, this kind of solution is not suitable, due to limitations, mostly regarding bandwidth, computation power, and available storage space. The aim of this paper is to present a solution for providing powerful reasoning mechanisms accessible from mobile applications and involving data from several heterogeneous sources. By adapting contents to time and location, mobile web information systems can not only increase the value and suitability of the service itself, but can substantially reduce the amount of data delivered to users. Because many problems pertain to infrastructures and transportation in general and to way finding in particular, one cornerstone of the architecture is higher level reasoning on graph networks with the Multi-Paradigm Location Language MPLL. A mediation architecture is used as a “graph provider” in order to transfer the load of computation to the best suited component – graph construction and transformation for example being heavy on resources. Reasoning in general can be conducted either near the “source” or near the end user, depending on the specific use case. The concepts underlying the proposal described in this paper are illustrated by a typical and concrete scenario for web applications