Is there a simple (meaning, memorable and not just a lot of crunching through probability formulas) proof that a variable is independent of the other variables in the network, given its Markov blanket?
A Markov Blanket is a set of variables that can fully predict the value of a target variable in a network, while excluding all other variables in the network.
Variable independence can be proven in a network by showing that the Markov Blanket of a target variable does not include any of its descendants or parents. This means that the target variable is independent of all other variables in the network given the variables in its Markov Blanket.
Proving variable independence in a network allows us to simplify complex networks and make predictions based on a smaller set of variables. It also helps in identifying causal relationships between variables.
Yes, a Markov Blanket can change over time as the values of variables in a network change. A variable that was not previously part of a Markov Blanket may become a part of it as its value affects the target variable.
One limitation is that Markov Blankets can only be used to prove conditional independence, where the target variable is independent of all other variables given the variables in its Markov Blanket. This may not hold true for all types of data. Additionally, the accuracy of the results depends on the quality and completeness of the data used to construct the network.