The Slippery Math of Causation
quantamagazine.org
quantamagazine.org
If I want to learn causal statistics, for use in ML, which school of thought would be more useful? I don't mean to prompt any causal flame wars, but it isn't obvious which approach is more useful.
[1] https://www.amazon.com/Book-Why-Science-Cause-Effect/dp/046509760X
[2] https://www.amazon.com/Causality-Reasoning-Inference-Judea-Pearl/dp/052189560X
[3] https://www.amazon.com/Causal-Inference-Statistics-Judea-Pearl/dp/1119186846
[4] https://www.amazon.com/Causal-Inference-Statistics-Biomedical-Sciences/dp/0521885884(btw this is in no way a "standardized" answer, just my opinion about how to start with the basics)
[0] In saying this I'm assuming neither one is outright wrong.
This other school-of-thought business (Bayesians vs. frequentists, pilot waves vs many worlds vs Copenhagen, everything like them) means choosing between different sets of words to describe the same thing. You are left with one of two cases: either they can be shown equivalent (in which case people are prone to keep on arguing over which one is better), or they are different (in which case one is wrong.)
So as a practical matter, you have to work in a better language, because the difference between spending 30 years to learn something and 30,000 years is quite significant.
Because the total amount of phenomenon explainable is too large for any theory, you cannot test or even hold entire concepts of "what each theory says" in your mind.
Schools of science form into communities which determine what is deemed "in scope", what are the grounding frameworks and concepts of the theories that explain the foundational phenomenon really well, informally what is out of scope, and the border territory of active research anomalies.
I only bring it up because I think it's one of the few works of genius and insight into how science and knowledge actually works in practice.
At the far end of "models work very well and the epistemology is solid," physics solves this problem by assigning different people to each phenomenological class (organized by the engineering similarity of the experimental devices needed to probe them) and then using math to check that everyone's individual confirmation of the theory in their area fits in correctly to the bigger picture. As a result even though the frontier of physics is too large for any one person to know, the confirmation of the standard model has been built into an unbroken surface that reaches all the way from the highest energies achieved to chemistry and astronomy.
When you have a theory like that, you can prove mathematically that it is equivalent to other theories. Then, the enlightened can stop arguing about which one is "truer!" If you have two theories that only exist in the form of English sentences (this was true of psychology in Freud's era) I can't imagine what an equivalence proof would look like, even if it would be possible. Fields where you can't formalize anything tend to have philosophies that look more and more like critical theory as you move further and further from pure logic. At the far end, the empiricism is completely phenomenological and the theory is nothing but literature with no predictive power (and as a result, the only way to choose between them is by disguising aesthetic arguments as appeals to this-or-that). I can't think of any fields that didn't look like that in their infancy, and success has usually been associated with progress away from that.
That's an example of how multiple equivalent formulations of the same theory can be useful for different things even though they are ultimately equivalent.
If you'd like to learn more, just use https://www.hsph.harvard.edu/miguel-hernan/causal-inference-.... It's an awesome resource and free.
Bertrand Russel, On The Notion Of Cause
Proceedings of the Aristotelian Society
New Series, Vol. 13 (1912 - 1913), pp. 1-26
It's also surprisingly funny.
[1] contains a good overview of this that presents Russel and critics (Salmon et. al). (I prefer that philosophy be taken in context rather than from the mouth of a particular philosopher).
https://users.drew.edu/jlenz/notion-of-cause/br-notion-of-ca...
Thanks for calling attention to this - it is interesting (and funny).
Sugihara's method is a way of quantifying causal relationships in nonlinear systems with attractors that would be cumbersome to model (hence the "equation free" description).
Pearl's Bayesian Statistics and Do-Calculus gives us a way to compute likelihoods around different observed events to give us some more insight into these mechanisms but from my reading so far, never give concrete solutions to when we should determine an action is not relevant.
Not relevant to what? What is the specific problem that Pearl does not resolve?
If there is no human there to blame do we then say that the cause is a coincidental combination of multiple spontaneous conditions, all necessary but not sufficient by themselves.