University of Michigan - Ann Arbor

A Markov blanket of a target variable is defined as the smallest subset of variables such that no variable outside this set contributes any additional information about the target variable. Let the Markov blanket be denoted by $$MB(Y)$$ where $$Y$$ is the target variable. Let $$\bar{MB(Y)}$$ be the complement of $$MB(Y)$$ in the universe of variables in the model. Then, $$P(Y|MB(Y), \bar{MB(Y)}) = P(Y|MB(Y))$$.

Markov Blanket

More application based, but I enjoyed reading about the approach : 
[arxiv.org/abs/2002.09414](https://arxiv.org/abs/2002.09414) 

Directed Acyclic Graphs and causal thinking in clinical risk prediction modeling

Image : Markov Blanket

In clinical risk prediction modeling, utilizing the Markov blanket of an outcome variable can optimize predictions. Evaluations of different logistic regression tools yield the following results:

1. Lasso regression selects exactly the Markov blanket at least 10% of the time.
2. Markov blanket logistic regression demonstrates better performance than other models while consistently requiring fewer predictor variables.
3. The Markov blanket model achieves the lowest Integrated Calibration Index, indicating superior model calibration.

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