10,063 research outputs found
Causal Dependence Tree Approximations of Joint Distributions for Multiple Random Processes
We investigate approximating joint distributions of random processes with
causal dependence tree distributions. Such distributions are particularly
useful in providing parsimonious representation when there exists causal
dynamics among processes. By extending the results by Chow and Liu on
dependence tree approximations, we show that the best causal dependence tree
approximation is the one which maximizes the sum of directed informations on
its edges, where best is defined in terms of minimizing the KL-divergence
between the original and the approximate distribution. Moreover, we describe a
low-complexity algorithm to efficiently pick this approximate distribution.Comment: 9 pages, 15 figure
Submodular Inference of Diffusion Networks from Multiple Trees
Diffusion and propagation of information, influence and diseases take place
over increasingly larger networks. We observe when a node copies information,
makes a decision or becomes infected but networks are often hidden or
unobserved. Since networks are highly dynamic, changing and growing rapidly, we
only observe a relatively small set of cascades before a network changes
significantly. Scalable network inference based on a small cascade set is then
necessary for understanding the rapidly evolving dynamics that govern
diffusion. In this article, we develop a scalable approximation algorithm with
provable near-optimal performance based on submodular maximization which
achieves a high accuracy in such scenario, solving an open problem first
introduced by Gomez-Rodriguez et al (2010). Experiments on synthetic and real
diffusion data show that our algorithm in practice achieves an optimal
trade-off between accuracy and running time.Comment: To appear in the 29th International Conference on Machine Learning
(ICML), 2012. Website:
http://www.stanford.edu/~manuelgr/network-inference-multitree
Distributed Dominating Set Approximations beyond Planar Graphs
The Minimum Dominating Set (MDS) problem is one of the most fundamental and
challenging problems in distributed computing. While it is well-known that
minimum dominating sets cannot be approximated locally on general graphs, over
the last years, there has been much progress on computing local approximations
on sparse graphs, and in particular planar graphs.
In this paper we study distributed and deterministic MDS approximation
algorithms for graph classes beyond planar graphs. In particular, we show that
existing approximation bounds for planar graphs can be lifted to bounded genus
graphs, and present (1) a local constant-time, constant-factor MDS
approximation algorithm and (2) a local -time
approximation scheme. Our main technical contribution is a new analysis of a
slightly modified variant of an existing algorithm by Lenzen et al.
Interestingly, unlike existing proofs for planar graphs, our analysis does not
rely on direct topological arguments.Comment: arXiv admin note: substantial text overlap with arXiv:1602.0299
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