Introduction

Learning a Bayesian network can be split into two main components: structure learning and parameter learning, both of which are implemented in bnlearn.

  • Structure learning: Given a set of data samples, estimate a Directed Acyclic Graph (DAG) that captures the dependencies between variables.

  • Parameter learning: Given a set of data samples and a DAG that captures the dependencies between variables, estimate the (conditional) probability distributions of the individual variables.

The library supports parameter learning for discrete nodes using:

  • Maximum Likelihood Estimation

  • Bayesian Estimation

Available Functions

  • Structure learning

  • Parameter learning

  • Inference

  • Sampling

  • Plotting

  • Network comparison

  • Loading BIF files

  • Conversion of directed to undirected graphs

Structure Learning Algorithms

bnlearn contains score-based, local discovery, Bayesian network, and constraint-based structure learning algorithms for discrete, fully observed networks.

Score-based approaches consist of two main components: * A search algorithm to optimize throughout the search space of all possible DAGs * A scoring function that indicates how well the Bayesian network fits the data

Score-based algorithms can be used with the following score functions for categorical data (multinomial distribution):

  • Bayesian Information Criterion (BIC)

  • K2 score

  • Score equivalent Dirichlet posterior density (BDeu)

Constraint-based Structure Learning Algorithms

Constraint-based structure learning constructs a DAG by identifying independencies in the dataset using hypothesis tests, such as the chi-square test statistic. This approach relies on statistical tests and conditional hypotheses to learn independence among the variables in the model. The p-value of the chi-square test represents the probability of observing the computed chi-square statistic, given the null hypothesis that X and Y are independent given Z. This can be used to make independence judgments at a given significance level. An example of a constraint-based approach is the PC algorithm, which starts with a complete, fully connected graph and removes edges based on the results of independence tests until a stopping criterion is achieved.

  • constraintsearch (cs)