The Slippery Math of Causation

https://www.quantamagazine.org/the-math-of-causation-puzzle-20180530/

by dfee • 8 years ago

124 23 8 years ago

kazinator• 8 years ago

If an catastrophic event occurs as a result of multiple necessary conditions, and one of those necessary conditions (even if not sufficient) is that some human was doing something they shouldn't have been doing, then of course it's that human's fault. Cause follows blame. We basically use "cause" as a synonym for "blame" in that situation.

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.

garmaine3• 8 years ago

I don't think that holds up if you reduce to simple examples that are easily analyzed. If a billiard ball is pushed, it is the contact of the thing that pushed it which caused its motion, an equal and opposite reaction by Newton's 3rd law. If you did statistical analysis you'd discover that the chances of a ball moving depend very highly on whether the last ball to end up in a net was matching suit (colored or striped). But that's not a causal connection in the same sense. There's a causality in this level of physics that works perfectly well. It's not a coincidental combination of multiple spontaneous conditions that the ball moved -- it moved because it got pushed, and if it hadn't been pushed it wouldn't have moved.

trhway• 8 years ago

that seems to be the whole core of those discussions - statistics, as a science, operates only with correlations and has nothing to do with causation. As long as one stays inside the domain of statistics, one can never say whether something is causation or not. Causation is subject matter of other sciences which study specific machinery of various causations.

AndrewKemendo• 8 years ago

The problem with Causation generally is that we choose arbitrary stopping points for "root causes," and fall into the Fallacy of the Single Cause.

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.

justinpombrio• 8 years ago

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?

cschmidt• 8 years ago

Since the OP is prompted by Judea Pearl's new book, I'll ask here. There seem to be at least two schools of thought in causal statistics. The first is championed by Judea Pearl [1,2,3] and the other by Donald Rubin [4].

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

imh• 8 years ago

Start with Rubin. Potential outcomes are more grounded and concretely interpretable. The epistemology is simple and won't get in your way, if you're inclined to dwell on those things. It also has the huge wealth of well developed techniques. Then move on to Pearl.

(btw this is in no way a "standardized" answer, just my opinion about how to start with the basics)

whatshisface3• 8 years ago

If there is more than one "school of thought," then there cannot be any real difference[0] between their results: because if there was, it would count as an empirical resolution between them. Everything else is metaphysical paint and should be taken according to taste.

[0] In saying this I'm assuming neither one is outright wrong.

tlb• 8 years ago

But one way can be vastly easier to get results than another other way. Even easy but wrong ways can be useful, such as Newtonian mechanics. (It's computationally infeasible to predict, eg, robot movements with quantum mechanics.)

ACow_Adonis• 8 years ago

Are you familiar with Thomas Kuhn? I ask because he wrote a book basically arguing that's not how science works at all.

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.

stdbrouw• 8 years ago

I studied Pearl and Rubin in college and didn't find them to be particularly antagonistic, though indeed they use somewhat different terminology and emphasize different things.

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.

olavolav• 8 years ago

Should any of you care for a more philosophical treatment of the idea of "cause", then I can wholeheartedly recommend:

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.

https://www.jstor.org/stable/4543833

Karrot_Kream• 8 years ago

This is a form of philosophy specifically known as causal processes.

[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).

1: https://plato.stanford.edu/entries/causation-process/

leephillips• 8 years ago

Here is a copy of the Russel paper free for all:

https://users.drew.edu/jlenz/notion-of-cause/br-notion-of-ca...

Thanks for calling attention to this - it is interesting (and funny).

blurbleblurble• 8 years ago

Just wanted to throw out a related Quanta article about Sugihara's method: https://www.quantamagazine.org/chaos-theory-in-ecology-predi...

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).

whitten• 8 years ago

So has anyone looked into the issues involved in explaining this level of causation to any AI systems? It seems this might be work, but interesting.

The Slippery Math of Causation

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