
The Slippery Math of Causation - dfee
https://www.quantamagazine.org/the-math-of-causation-puzzle-20180530/
======
cschmidt
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

~~~
whatshisface
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.

~~~
ACow_Adonis
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.

~~~
whatshisface
> _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._

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.

~~~
testvox
> 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)

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.

------
olavolav
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](https://www.jstor.org/stable/4543833)

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

[https://users.drew.edu/jlenz/notion-of-cause/br-notion-of-
ca...](https://users.drew.edu/jlenz/notion-of-cause/br-notion-of-cause.html)

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

------
macawfish
Just wanted to throw out a related Quanta article about Sugihara's method:
[https://www.quantamagazine.org/chaos-theory-in-ecology-
predi...](https://www.quantamagazine.org/chaos-theory-in-ecology-predicts-
future-populations-20151013/)

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).

------
AndrewKemendo
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
> 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?

------
kazinator
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.

~~~
garmaine
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
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.

~~~
garmaine
I would suggest reading up on Judea Pearl’s Caudality, which is a complete
treatment of how to integrate a useful notion of causality into statistical
analysis. It can be done; it’s just not common practice.

~~~
garmaine
*Causality

------
whitten
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.

