# An Improved Admissible Heuristic for Learning Optimal Bayesian Networks

@inproceedings{Yuan2012AnIA, title={An Improved Admissible Heuristic for Learning Optimal Bayesian Networks}, author={Changhe Yuan and Brandon M. Malone}, booktitle={UAI}, year={2012} }

Recently two search algorithms, A* and breadth-first branch and bound (BFBnB), were developed based on a simple admissible heuristic for learning Bayesian network structures that optimize a scoring function. The heuristic represents a relaxation of the learning problem such that each variable chooses optimal parents independently. As a result, the heuristic may contain many directed cycles and result in a loose bound. This paper introduces an improved admissible heuristic that tries to avoid…

## 46 Citations

### An Improved Lower Bound for Bayesian Network Structure Learning

- Computer ScienceAAAI
- 2015

A new partition method based on information extracted from the potential optimal parent sets (POPS) of the variables of a data set can significantly improve the efficiency and scalability of heuristic search-based structure learning algorithms.

### Learning Optimal Bayesian Networks: A Shortest Path Perspective

- Computer ScienceJ. Artif. Intell. Res.
- 2013

An A* search algorithm that learns an optimal Bayesian network structure by only searching the most promising part of the solution space and a heuristic function that reduces the amount of relaxation by avoiding directed cycles within some groups of variables.

### Finding Optimal Bayesian Network Structures with Constraints Learned from Data

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- 2014

The observation that there is useful information implicit in the POPS is made, which shows that solving the constrained subproblems significantly improves the efficiency and scalability of heuristic search-based structure learning algorithms.

### Tightening Bounds for Bayesian Network Structure Learning

- Computer ScienceAAAI
- 2014

Methods for tightening the bounds of a breadth-first branch and bound algorithm by using more informed variablegroupings when creating the pattern databases and using an anytime learning algorithm are introduced.

### A Depth-First Branch and Bound Algorithm for Learning Optimal Bayesian Networks

- Computer ScienceGKR
- 2013

This work presents a new depth-first branch and bound algorithm that finds increasingly better solutions and eventually converges to an optimal Bayesian network upon completion and proves the optimality of these solutions about 10 times faster in some cases.

### Bidirectional heuristic search to find the optimal Bayesian network structure

- Computer Science, BusinessNeurocomputing
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### Evaluating Anytime Algorithms for Learning Optimal Bayesian Networks

- Computer ScienceUAI
- 2013

Several anytime heuristic search-based algorithms are adapted to learn Bayesian networks to show that the anytime window A* algorithm usually finds higher-quality, often optimal, networks more quickly than other approaches, and that, surprisingly, while generating networks with few parents per variable are structurally simpler, they are harder to learn.

### On Pruning for Score-Based Bayesian Network Structure Learning

- Computer ScienceAISTATS
- 2020

New non-trivial theoretical upper bounds for the BDeu score are derived that considerably improve on the state-of-the-art and are a promising addition to BNSL methods.

### Advances in Bayesian Network Learning using Integer Programming

- Computer ScienceUAI
- 2013

After relating this BN learning problem to set covering and the multidimensional 0-1 knapsack problem, the various steps taken to allow efficient solving of this IP are described.

### Learning Bayesian Networks with Thousands of Variables

- Computer ScienceNIPS
- 2015

A novel algorithm that effectively explores the space of possible parent sets of a node on the basis of an approximated score function that is computed in constant time and an improvement of an existing ordering-based algorithm for structure optimization.

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