2017 Lecture 4 : October 9 , 2017
نویسنده
چکیده
We consider a set of random variables in a particular relationship and its consequences for mutual information. An ordered tuple of random variables (X, Y, Z) is said to form a Markov chain, written as X → Y → Z, if X and Z are independent conditioned on Y. Here, we can think of Y as being sampled given the knowledge of X, and Z being sampled given the knowledge of Y (but not using the “history” about X). Note that although the notation X → Y → Z (and also the above description) makes it seem like this is only a Markov chain the forward order, the conditional independence definition implies that if X → Y → Z is Markov chain, then so is Z → Y → X. This is sometimes to written as X ↔ Y ↔ Z to clarify that the variables form a Markov chain in both forward and backward orders. The following inequality shows that information about the starting point cannot increase as we go further in a Markov chain.
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