• Corpus ID: 12119394

On learning the structure of Bayesian Networks and submodular function maximization

@article{Caravagna2017OnLT,
  title={On learning the structure of Bayesian Networks and submodular function maximization},
  author={Giulio Caravagna and Daniele Ramazzotti and Guido Sanguinetti},
  journal={ArXiv},
  year={2017},
  volume={abs/1706.02386}
}
Learning the structure of dependencies among multiple random variables is a problem of considerable theoretical and practical interest. In practice, score optimisation with multiple restarts provides a practical and surprisingly successful solution, yet the conditions under which this may be a well founded strategy are poorly understood. In this paper, we prove that the problem of identifying the structure of a Bayesian Network via regularised score optimisation can be recast, in expectation… 
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References

SHOWING 1-10 OF 48 REFERENCES
Ordering-Based Search: A Simple and Effective Algorithm for Learning Bayesian Networks
TLDR
It is shown that ordering-based search outperforms the standard baseline, and is competitive with recent algorithms that are much harder to implement.
Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks
TLDR
This paper shows how to efficiently compute a sum over the exponential number of networks that are consistent with a fixed order over network variables, and uses this result as the basis for an algorithm that approximates the Bayesian posterior of a feature.
Data Analysis with Bayesian Networks: A Bootstrap Approach
TLDR
This paper proposes Efron's Bootstrap as a computationally efficient approach for answering confidence measures on features of Bayesian networks, and proposes to use these confidence measures to induce better structures from the data, and to detect the presence of latent variables.
Network inference using informative priors
TLDR
This article addresses the question of incorporating prior information into network inference with focus on directed models called Bayesian networks, and introduces prior distributions on graphs capable of capturing information regarding network features including edges, classes of edges, degree distributions, and sparsity.
Improving the structure MCMC sampler for Bayesian networks by introducing a new edge reversal move
TLDR
A new and more extensive edge reversal move is proposed in the original structure space, and it is shown that this significantly improves the convergence of the classical structure MCMC scheme.
An analysis of approximations for maximizing submodular set functions—I
TLDR
It is shown that a “greedy” heuristic always produces a solution whose value is at least 1 −[(K − 1/K]K times the optimal value, which can be achieved for eachK and has a limiting value of (e − 1)/e, where e is the base of the natural logarithm.
A Bayesian method for the induction of probabilistic networks from data
TLDR
This paper presents a Bayesian method for constructing probabilistic networks from databases, focusing on constructing Bayesian belief networks, and extends the basic method to handle missing data and hidden variables.
Learning Gaussian Networks
Using Bayesian Networks to Analyze Expression Data
TLDR
This paper proposes a new framework for discovering interactions between genes based on multiple expression measurements, and presents an efficient algorithm capable of learning such networks and statistical method to assess confidence in their features.
Gene Regulatory Network Reconstruction Using Bayesian Networks, the Dantzig Selector, the Lasso and Their Meta-Analysis
TLDR
A simple yet very powerful meta-analysis is proposed, which combines a wide panel of methods ranging from Bayesian networks to penalised linear regressions to analyse gene regulatory networks from different genetical genomics data sets and was ranked first among the teams participating in Challenge 3A.
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