All Questions
Tagged with conditional-independence causality
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Why does dimensionality affect significance and effect size in a Full Conditional Independence (FullCI) test?
The 2018 Runge et al paper titled "Detecting causal associations in large non linear time series datasets" describes the PCMCI method. It compares the new PCMCI method with another method ...
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Conditional expectation function and causal inference
!For the question itself skip to the last paragraph!
It is my understanding that iff we have a model of the form $$Y = m(X) + e$$ and $E[e|X] = 0$ we know that $m(X)$ is the conditional expectation ...
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Testing for conditional independence with nonlinear relationships
I am reading about the IC and IC* (Inductive Causation) algorithms for discovering DAGs from observations. The first step of the algorithm is for each pair of variables a and b, search for a set of ...
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Is treatment conditionally independent from outcome in Single Experiment Design?
I'm reading this slides.
At slide 10 there is written that in "Single Experiment Design" we assume "Randomization of treatment", that is:
$ \{ Y_i(t,m),M_i(t') \} \perp T_i \lvert ...
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Is A independent of B conditioned on B?
Does $A \perp\!\!\!\!\!\!\perp B | B$ always hold?
Part of me is like yes: if we know the value of $B$, then more information about $B$ can't tell us anything about $A$, and vice versa.
Consider this ...
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What's the relationship between statement "Z causes both X and Y" and "X and Y are independent given Z"?
Suppose I have two statements:
Statement 1: Random variable Z is the common cause for random variable X and Y (Z causes both X and Y)
Statement 2: Random variable X and Y are (conditionally) ...
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Clarify, with example, completeness conjecture by Pearl and Paz
I was going through Probabilistic Reasoning In Intelligent Systems by Judea Pearl. A completeness conjecture (for which no complete proof is there as yet, but has been found to be true generally, as ...
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AIPW and Cross-fitting (Stanford stat361)
I am reading lecture note (Stanford stat361: https://web.stanford.edu/~swager/stats361.pdf) written by Stefan Wager. At page 23-24 the author states dependent summands become independent after ...
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Causality: Models, Reasoning, and Inference: Notation Question Concerning Graphoids
$\newcommand{\ci}{\!\perp\!\!\!\perp\!}$On page 11 of the book in the title, Pearl introduces the Dawid notation for conditional independence: $(X\ci Y|Z)_P$ if and only if $P(x|y,z)=P(x|z)$ for all ...
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Expectation of potential outcomes formula
In Mostly Harmless Econometrics, the author uses the following identity to derive an estimator for the causal effect:
$$E \left[ \frac{Y_i D_i} {p(X_i)} \right] = E \left[Y_{1i} \right]$$
where:
$...
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