Markov Blankets

In statistics and Machine Learning, the __Markov blanket__ for a vertex (graph theory) in a graphical model contains all the variables that shield the node from the rest of the network. This means that the Markov blanket of a node is the only knowledge needed to predict the behavior of that node and its children. The term was coined by Judea Pearl in 1988 - wikipedia

In a Bayesian network, the Markov blanket of node ''A'' includes its parents, children and the other parents of all of its children - wikimedia

# Description In a Bayesian network, the values of the parents and children of a node evidently give information about that node. However, its children's parents also have to be included, because they can be used to explain away the node in question. In a Markov random field, the Markov blanket for a node is simply its adjacent (or neighboring) nodes. In a Dependency network (graphical model), the Markov blanket for a node is simply the set of its parents.

The concept of Markov Blankets in incorporated within the Free Energy Principle as the means by which an increasing complex Meaning Matrix is developed to allow increasing accuracy in response to complexity - creating Overlapping Blankets

digraph { layout=dot rankdir=TB overlap=false concentrate=false bgcolor=lightblue // splines=" " node [shape=box style=rounded] label=" \nMarkov Blanket" "Central\nNode" [color=red] "Parents of\nCentral\nNode" -> "Central\nNode" -> "Children\nof Central\nNode" "Other\nParents of\nCentral Node's\nChildren" -> "Children\nof Central\nNode" }

Keep in mind that there can be many more than two parents, many children, and many many other parents of central node's children. So while this blanket removes uncountable complexity, it still admits much complexity. Bayes Theorem further eliminates complexity (uncertainty) while still admitting much uncertainty.

The next task is to make a simple graph illustrating nesting of Markov Blankets and a practical accompanying story. Oh, and it would be nice to illustrate the power of Bayes Theorem (effects of history) in these simple (small) graphs. :>)

# Links - royalsocietypublishing.org