# Exact Bayesian Structure Discovery in Bayesian Networks

@article{Koivisto2004ExactBS, title={Exact Bayesian Structure Discovery in Bayesian Networks}, author={M. Koivisto and K. Sood}, journal={J. Mach. Learn. Res.}, year={2004}, volume={5}, pages={549-573} }

Learning a Bayesian network structure from data is a well-motivated but computationally hard task. We present an algorithm that computes the exact posterior probability of a subnetwork, e.g., a directed edge; a modified version of the algorithm finds one of the most probable network structures. This algorithm runs in time O(n 2n + nk+1C(m)), where n is the number of network variables, k is a constant maximum in-degree, and C(m) is the cost of computing a single local marginal conditional… Expand

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#### References

SHOWING 1-10 OF 31 REFERENCES

Being Bayesian About Network Structure. A Bayesian Approach to Structure Discovery in Bayesian Networks

- Mathematics, Computer Science
- Machine Learning
- 2004

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. Expand

A Bayesian Approach to Learning Bayesian Networks with Local Structure

- Computer Science, Mathematics
- UAI
- 1997

A Bayesian approach to learning Bayesian networks that contain the more general decision-graph representations of the CPDs is investigated, and how to evaluate the posterior probability-- that is, the Bayesian score--of such a network, given a database of observed cases is described. Expand

Learning Bayesian Networks: Search Methods and Experimental Results

- Computer Science
- 1995

A metric for computing the relative posterior probability of a network structure given data developed by Heckerman et al. (1994a,b,c) has a property useful for inferring causation from data and is described. Expand

Learning Bayesian Networks: The Combination of Knowledge and Statistical Data

- Computer Science, Mathematics
- Machine Learning
- 2004

A methodology for assessing informative priors needed for learning Bayesian networks from a combination of prior knowledge and statistical data is developed and how to compute the relative posterior probabilities of network structures given data is shown. Expand

On Inclusion-Driven Learning of Bayesian Networks

- Mathematics, Computer Science
- J. Mach. Learn. Res.
- 2003

This paper introduces a condition for traversal operators, the inclusion boundary condition, which guarantees that the search strategy can avoid local maxima and carries out a set of experiments that show empirically the benefit of striving for the inclusion order when learning Bayesian networks from data. Expand

Optimal Structure Identification With Greedy Search

- Mathematics, Computer Science
- J. Mach. Learn. Res.
- 2002

This paper proves the so-called "Meek Conjecture", which shows that if a DAG H is an independence map of another DAG G, then there exists a finite sequence of edge additions and covered edge reversals in G such that H remains anindependence map of G and after all modifications G =H. Expand

Searching for Bayesian Network Structures in the Space of Restricted Acyclic Partially Directed Graphs

- Mathematics, Computer Science
- J. Artif. Intell. Res.
- 2003

This paper proposes a new local search method that uses a different search space, and which takes account of the concept of equivalence between network structures: restricted acyclic partially directed graphs (RPDAGs). Expand

A Bayesian method for the induction of probabilistic networks from data

- Computer Science
- Machine Learning
- 2004

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. Expand

Computer-based probabilistic-network construction

- Computer Science
- 1992

This dissertation demonstrates that nonparametric, efficient, computer-based algorithms for determining the important associations among variables in a domain are conceptually feasible, robust to noise, computationally efficient, theoretically sound, and that they generate models that can classify new cases accurately. Expand

A Bayesian Approach to Causal Discovery

- Mathematics
- 2006

We examine the Bayesian approach to the discovery of causal DAG models and compare it to the constraint-based approach. Both approaches rely on the Causal Markov condition, but the two differ… Expand