Markov Blanket

Context

• Unlike Unsupervised Structural Learning, the objective of Supervised Learning is not to find the best representation of the joint probability distribution sampled by the observations ("particles") described in the data set, but rather to find the best probabilistic characterization of a Target Node.
• Among the available Supervised Learning algorithms offered in BayesiaLab, the Markov Blanket Learning algorithms are the most advanced.
• Their main objective is to efficiently identify the subset of nodes, the Markov Blanket, that makes the Target Node conditionally independent of all other nodes.

Markov Blanket Definition

• The Markov Blanket of the Target Node had the following characteristics:
  • Its Parents block the information flow coming from the indirect ancestors;
  • Its Children block the information flow coming from the indirect descendants;
  • Its Spouses block the conditional information flow coming from the ancestors and descendants of the spouses when the Children are observed.

Markov Blanket Algorithms

• Three Markov Blanket Learning algorithms are available in BayesiaLab.

The Markov Blanket Algorithm

• The Markov Blanket algorithm returns the graph in which the Target Node is connected to its Markov Blanket, i.e., the algorithm identifies the Markov Blanket of the Target Node.

The Augmented Markov Blanket Algorithm

• The Augmented Markov Blanket algorithm adds an Unsupervised Structural Learning algorithm to find the dependencies between the nodes in the Markov Blanket of the Target Node.
• Adding these additional relationships can help improve the predictive performance of the model.

The Minimal Augmented Markov Blanket Algorithm

• The Minimal Augmented Markov Blanket Algorithm algorithm also applies an Unsupervised Structural Learning algorithm to the nodes in the Markov Blanket of the Target Node.
• However, from the nodes in the resulting (now augmented) network, the algorithm selects the Markov Blanket of the Target Node.
• This further selection can be useful because the Markov Blanket returned by the Markov Blanket algorithm alone can contain ancestors and descendants that have more than one path to the Target Node, making interpration challenging.
• The Minimal Augmented Markov Blanket algorithm can therefore produce a Markov Blanket that is closer to the to the true data-generating process.

Constraints

As of BayesiaLab version 9.0, the Markov Blanket algorithms can take into account Arc Constraints defined by

• Forbidden Arcs
• Temporal Indices