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Questions tagged [conditional-independence]

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Conditional independence problem for poisson random variables

I have this problem: Let $X = V + W$ and $Y = V + Z$ where $V, W, Z$ are independent Pois($\lambda$) random variables. I found that $Cov(X, Y) = Var(V) = \lambda$ It now asks to find whether $X$ ...
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If outputs are independent why can we drop the condition on other outputs' inputs?

In a book the author is trying to explain why we cannot assume independence among outputs but rather conditionally independence. He gives this example: Imagine we had values of all Olympic years ...
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Do GGMs model partial correlation or conditional independence or both?

Post that says partial correlation != conditional dependence/independence: https://www.quora.com/Does-a-partial-correlation-of-0-imply-conditional-independence Post above points to following paper: ...
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Naive bayes example by hand

Given the following data ...
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Conditional independence and joint distributions in graphical models

I'm reading Deep Learning by Ian Goodfellow and Yoshua Bengio and Aaron Courville. In chapter 3 about graphical models, to reduce the model complexity, we assume that certain conditional independence ...
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Conditions Mutual Information and Confounding Effect

Given that conditional mutual information (CMI) I(A,B |C) is the information shared between A, and B given C, does this consider the confounding effect -if any - that C introduces? In other words, ...
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Chi-Squared Statistic to test for conditional independence

How can compute the chi-square statistic between the random variables X and Y given an evidence variable Z? I want to test if X & Y are conditionally independent given Z. Assume all X,Y, Z are ...
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Conditional Independence Example

Is there a canonical example of data which are conditionally independent? In other words, $X_1,\ldots,X_p$ are mutually independent given $Y$. This is the foundational assumption of the naive Bayes ...
My goal is to check if two variables $X$ and $Y$ are conditionally independent given $Z$. For simplicity, let's assume the joint distribution is multivariate normal. In this case, we can compute ...
Is $X \perp\!\!\!\perp Y$ a conditional independence, arguing that the independence is conditioned on an empty set of random variables? If so, does that mean that an unconditional independence is ...