### Abstract

We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to score-based structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and is given by the probability that a conditional independence test correctly shows that an edge cannot exist. What really distinguishes this new scoring function from earlier work is that it has the property of becoming computationally easier to maximize as the amount of data increases. We prove a polynomial sample complexity result, showing that maximizing this score is guaranteed to correctly learn a structure with no false edges and a distribution close to the generating distribution, whenever there exists a Bayesian network which is a perfect map for the data generating distribution. Although the new score can be used with any search algorithm, we give empirical results showing that it is particularly effective when used together with a linear programming relaxation approach to Bayesian network structure learning.

Original language | English (US) |
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Title of host publication | Uncertainty in Artificial Intelligence - Proceedings of the 29th Conference, UAI 2013 |

Pages | 112-121 |

Number of pages | 10 |

State | Published - 2013 |

Event | 29th Conference on Uncertainty in Artificial Intelligence, UAI 2013 - Bellevue, WA, United States Duration: Jul 11 2013 → Jul 15 2013 |

### Other

Other | 29th Conference on Uncertainty in Artificial Intelligence, UAI 2013 |
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Country | United States |

City | Bellevue, WA |

Period | 7/11/13 → 7/15/13 |

### Fingerprint

### ASJC Scopus subject areas

- Artificial Intelligence

### Cite this

*Uncertainty in Artificial Intelligence - Proceedings of the 29th Conference, UAI 2013*(pp. 112-121)

**SparsityBoost : A new scoring function for learning Bayesian network structure.** / Brenner, Eliot; Sontag, David.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Uncertainty in Artificial Intelligence - Proceedings of the 29th Conference, UAI 2013.*pp. 112-121, 29th Conference on Uncertainty in Artificial Intelligence, UAI 2013, Bellevue, WA, United States, 7/11/13.

}

TY - GEN

T1 - SparsityBoost

T2 - A new scoring function for learning Bayesian network structure

AU - Brenner, Eliot

AU - Sontag, David

PY - 2013

Y1 - 2013

N2 - We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to score-based structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and is given by the probability that a conditional independence test correctly shows that an edge cannot exist. What really distinguishes this new scoring function from earlier work is that it has the property of becoming computationally easier to maximize as the amount of data increases. We prove a polynomial sample complexity result, showing that maximizing this score is guaranteed to correctly learn a structure with no false edges and a distribution close to the generating distribution, whenever there exists a Bayesian network which is a perfect map for the data generating distribution. Although the new score can be used with any search algorithm, we give empirical results showing that it is particularly effective when used together with a linear programming relaxation approach to Bayesian network structure learning.

AB - We give a new consistent scoring function for structure learning of Bayesian networks. In contrast to traditional approaches to score-based structure learning, such as BDeu or MDL, the complexity penalty that we propose is data-dependent and is given by the probability that a conditional independence test correctly shows that an edge cannot exist. What really distinguishes this new scoring function from earlier work is that it has the property of becoming computationally easier to maximize as the amount of data increases. We prove a polynomial sample complexity result, showing that maximizing this score is guaranteed to correctly learn a structure with no false edges and a distribution close to the generating distribution, whenever there exists a Bayesian network which is a perfect map for the data generating distribution. Although the new score can be used with any search algorithm, we give empirical results showing that it is particularly effective when used together with a linear programming relaxation approach to Bayesian network structure learning.

UR - http://www.scopus.com/inward/record.url?scp=84888177974&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84888177974&partnerID=8YFLogxK

M3 - Conference contribution

SP - 112

EP - 121

BT - Uncertainty in Artificial Intelligence - Proceedings of the 29th Conference, UAI 2013

ER -