From Sparse Data to Bayesian Networks: A Statistical Learning Approach

Title: From Sparse Data to Bayesian Networks: A Statistical Learning Approach

Research Question: Can we develop a method to learn the dependencies among random variables from sparse data, suggesting that these dependencies can be described by a simple graph with a small in-degree, and provide reliability bounds on the error of the estimated joint measure?

Methodology: The authors propose a method to learn the dependencies among random variables by considering the case where sparse data strongly suggests that the probabilities can be described by a simple Bayesian network, i.e., a graph with a small in-degree (number of nodes that have an arrow pointing to them). They calculate bounds on the VC dimension of the set of those probability measures that correspond to simple graphs, which allows them to select networks by structural risk minimization and provides reliability bounds on the error of the estimated joint measure.

Results: The complexity for searching the optimal Bayesian network of in-degree ∆ increases only polynomially in the number of random variables for constant ∆, and the optimal joint measure associated with a given graph can be found by convex optimization.

Implications: This research has significant implications for the field of statistical learning. It provides a method to learn the dependencies among random variables from sparse data, suggesting that these dependencies can be described by a simple graph with a small in-degree. This method allows for the selection of networks by structural risk minimization and provides reliability bounds on the error of the estimated joint measure, which is crucial for the accuracy of the learned model.

Link to Article: https://arxiv.org/abs/0309015v1 Authors: arXiv ID: 0309015v1