# Scalable Bayesian Network Structure Learning with Splines

@article{Sharma2021ScalableBN, title={Scalable Bayesian Network Structure Learning with Splines}, author={Charupriya Sharma and P. V. Beek}, journal={ArXiv}, year={2021}, volume={abs/2110.14626} }

A Bayesian Network (BN) is a probabilistic graphical model consisting of a directed acyclic graph (DAG), where each node is a random variable represented as a function of its parents. We present a novel approach capable of learning the global DAG structure of a BN and modelling linear and non-linear local relationships between variables. We achieve this by a combination of feature selection to reduce the search space for local relationships, and extending the widely used score-and-search…

## References

SHOWING 1-10 OF 33 REFERENCES

A Score-and-Search Approach to Learning Bayesian Networks with Noisy-OR Relations

- Computer SciencePGM
- 2020

This paper provides an effective gradient descent algorithm to score a candidate noisy-OR using the widely used BIC score and provides pruning rules that allow the search to successfully scale to medium sized networks.

Learning Bayesian networks with local structure, mixed variables, and exact algorithms

- Computer ScienceInt. J. Approx. Reason.
- 2019

It is shown that under modest restrictions on the possible branchings in the tree structure, it is feasible to find a structure that maximizes a Bayes score in a range of moderate-size problem instances, which enables global optimization of the Bayesian network structure, including the local structure.

A* Lasso for Learning a Sparse Bayesian Network Structure for Continuous Variables

- Computer Science, MathematicsNIPS
- 2013

A single-stage method, called A* lasso, is proposed that recovers the optimal sparse Bayesian network structure by solving a single optimization problem with A* search algorithm that uses lasso in its scoring system.

Machine Learning of Bayesian Networks Using Constraint Programming

- Computer ScienceCP
- 2015

This paper proposes an improved constraint model that includes powerful dominance constraints, symmetry-breaking constraints, cost-based pruning rules, and an acyclicity constraint for effectively pruning the search for a minimum cost solution to the model.

A Bayesian Approach to Learning Bayesian Networks with Local Structure

- Computer Science, MathematicsUAI
- 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.

Bayesian networks with a logistic regression model for the conditional probabilities

- Computer Science, MathematicsInt. J. Approx. Reason.
- 2008

Order logistic regression can be used to restrict the conditional probabilities of a Bayesian network for discrete variables when the categories of a variable are ordered, resulting in even more parsimonious models.

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.

Exploiting Causal Independence in Bayesian Network Inference

- Mathematics, Computer ScienceJ. Artif. Intell. Res.
- 1996

A notion of causal independence is presented that enables one to further factorize the conditional probabilities into a combination of even smaller factors and consequently obtain a finer-grain factorization of the joint probability.

Learning Bayesian Networks with Local Structure

- Computer Science, MathematicsUAI
- 1996

A novel addition to the known methods for learning Bayesian networks from data that improves the quality of the learned networks and indicates that learning curves characterizing the procedure that exploits the local structure converge faster than these of the standard procedure.

Causal Discovery from Databases with Discrete and Continuous Variables

- Computer ScienceProbabilistic Graphical Models
- 2014

This work proposes a novel method for the efficient computation of BIC scores for hybrid Bayesian networks and demonstrates the accuracy and efficiency of this approach for causal discovery on simulated data as well as on real-world data from the ADHD-200 competition.