Markov blanket

In statistics and machine learning, when one wants to infer a random variable with a set of variables, usually a subset is enough, and other variables are useless.

Such a subset that contains all the useful information is called a Markov blanket.

If a Markov blanket is minimal, meaning that it cannot drop any variable without losing information, it is called a Markov boundary.

Identifying a Markov blanket or a Markov boundary helps to extract useful features.

The terms of Markov blanket and Markov boundary were coined by Judea Pearl in 1988.

A Markov blanket of a random variable

in a random variable set

, conditioned on which other variables are independent with

In general, a given Markov blanket is not unique.

The Markov boundary of a node

in a Bayesian network is the set of nodes composed of

In a Markov random field, the Markov boundary for a node is the set of its neighboring nodes.

In a dependency network, the Markov boundary for a node is the set of its parents.

The Markov boundary always exists.

Under some mild conditions, the Markov boundary is unique.

However, for most practical and theoretical scenarios multiple Markov boundaries may provide alternative solutions.

[2] When there are multiple Markov boundaries, quantities measuring causal effect could fail.