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Given a set of random variables $X = \{x_1, x_2, \dots, x_n\}$. If the conditional entropy for all $Y \subset X - \{X_i\}$ where $|Y| \leq 5$. How to approximate conditional entropy when $|Y| = 10$ based on the given knowledge? Is it possible to approximate better than $H(X_i | X - \{X_i\})$ ?

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    $\begingroup$ I don't understand what you are asking. I cannot understand the sentence "If the conditional entropy" -- that sentence has no verb. Are some words missing? Conditional entropy of what random variable, conditioned on what random variable? Also, what do you know about the random variable and the random process generating them? How are they specified? What exactly is the input to the algorithm? Are you given the joint distribution of $X$? A way to sample from that distribution? Something else? It's hard to tell what you are asking; please edit the question. $\endgroup$ – D.W. Feb 20 '17 at 22:07

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