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Activity Number:
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31
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Type:
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Contributed
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Date/Time:
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Sunday, August 2, 2009 : 2:00 PM to 3:50 PM
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Sponsor:
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Section on Statistical Learning and Data Mining
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| Abstract - #304711 |
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Title:
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Penalized Likelihood Methods for Estimation of Directed Acyclic Graphs with Applications to Biological Networks
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Author(s):
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Ali Shojaie*+ and George Michailidis
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Companies:
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University of Michigan and University of Michigan
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Address:
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269 West Hall, 1085 South University Ave, Ann Arbor, MI, 48109,
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Keywords:
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Directed Acyclic Graphs ; Penalized Likelihood ; Covariance Estimation ; Lasso ; Adaptive Lasso ; Biological Networks
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Abstract:
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Directed edges are commonly used to represent causal relationship among random variables in graphical models. Directed acyclic graphs (DAGs), also known as Bayesian networks are special classes of directed graphs with no directed cycles. Estimation of DAGs from observational data is in general an NP-hard problem and few algorithms are available for estimation of DAGs with large number of nodes. In this paper, we propose penalized likelihood methods for estimation of DAGs when the nodes exhibit a natural ordering. We study both lasso as well as adaptive lasso estimates and propose an efficient algorithm. Asymptotic properties of these estimators are discussed in the small n large p setting, as the number of nodes grows to infinity as a polynomial function of the sample size. The performance of the proposed estimates is compared to alternative methods using simulated as well as real data.
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