Learning Bayesian networks by hill climbing: efficient methods based on progressive restriction of the neighborhood

Bayesian networks have been widely used in many scientific fields for describing the conditional independence relationships for a large set of random variables. This letter proposes a novel algorithm, the so-called p-learning algorithm, for learning moral graphs for high-dimensional Bayesian networks. The moral graph is a Markov network representation of the Bayesian network and also the key to construction of the Bayesian network for constraint-based algorithms. The consistency of the p-learning algorithm is justified under the small- n, large- p scenario. The numerical results indicate that the p-learning algorithm significantly outperforms the existing ones, such as the PC, grow-shrink, incremental association, semi-interleaved hiton, hill-climbing, and max-min hill-climbing. Under the sparsity assumption, the p-learning algorithm has a computational complexity of O(p2) even in the worst case, while the existing algorithms have a computational complexity of O(p3) in the worst case.

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Bayesian Networks for Set-Based Collaborative Design

Volume 5: 35th Design Automation Conference, Parts A and B ◽

10.1115/detc2009-87541 ◽

2009 ◽

Cited By ~ 3

Author(s):

David Shahan ◽

Carolyn C. Seepersad

Keyword(s):

Bayesian Networks ◽

Design Process ◽

Collaborative Design ◽

Design Space ◽

Expert Knowledge ◽

Hill Climbing ◽

Local Networks ◽

Design Problems ◽

Potential Benefits ◽

Aerial Vehicle

A set-based approach to collaborative design is presented, in which Bayesian networks are used to represent promising regions of the design space. In collaborative design exploration, complex multilevel design problems are often decomposed into distributed subproblems that are linked by shared or coupled parameters. Collaborating designers often prefer conflicting values for these coupled parameters, resulting in incompatibilities that require substantial iteration to resolve, extending the design process lead time without guarantee of achieving a good design. In the proposed approach to collaborative design, each designer builds a locally developed Bayesian network that represents regions of interest in his design space. Then, these local networks are shared and combined with those of collaborating designers to promote more efficient local design space search that takes into account the interests of one’s collaborators. The proposed method has the potential to capture a designer’s preferences for arbitrarily shaped and potentially disconnected regions of the design space in order to identify compatible or conflicting preferences between collaborators and to facilitate a compromise if necessary. It also sets the stage for a flexible and concurrent design process with varying degrees of designer involvement that can support different designer strategies such as hill-climbing or region identification. The potential benefits are the capture of expert knowledge for future use as well as conflict identification and resolution. This paper presents an overview of the proposed method as well as an example implementation for the design of an unmanned aerial vehicle.

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