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Let's say that a data set has N random binary variables Xi and we want to infer which of these variables have a causal relationship with X1. The following table would describe the data, where each column is an observable moment in time... The dataset is very large and the number of observations can be as big as needed

X1 1 1 1 0 0 0 0
X2 0 1 0 1 1 0 1
X3 1 0 1 1 1 0 0
...
Xn 1 1 1 1 0 1 0

There is a population of M individuals, each of these individuals has a different table, but we can use these M individuals to develop the required statistics to infer causality (not correlation)

How can this be done?

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1 Answer 1

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I do not think you will get a satisfactory answer here. In fact, after thinking about the most appropriate stackexchange site for your question, I concluded that it is the philosophy stackexchange.

All joking aside, the question you are asking is very hard from multiple perspectives. To show causal relationships ideally you want randomized experiments and doing appropriate interventions. But you are essentially asking to determine the causal structure from observational data.

This is in general impossible, but at the same time it is a major open research question. In particular, if you are willing to assume that the true underlying causal graph has certain properties, then sometimes it becomes identifiable from observational data and you can answer questions as the one you asked. For more details you should consult current research in this area, e.g. Schölkopf's and Bühlmann's work.

Finally I also attach the obligatory XKCD comic:

causality xkcd

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