There are at least 13 ways to think about correlation Rodgers & Nicewander 1988 "Thirteen ways to look at the correlation coefficient" https://www.jstor.org/stable/pdf/2685263.pdf
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How to Think about Correlation?
31–40 of 60 posts
Re: How to Think about Correlation?
#32I don’t understand any of the responses I’m reading. The question isn’t asking for an intuitive understanding of correlation. He’s just complaining that only normalized values are presented.
Re: How to Think about Correlation?
#33Correlations are a profound part of our universe. When observing the universe, humans can never prove any facts about the universe. We can only establish correlations. Correlations between events that occur in our universe is the furthest "truth" we can establish about the universe short of a full on proof. What this means is that nothing in the physical universe can be proven. Proof is the domain of maths and logic,…
Well yeah this is deduction vs induction
Re: How to Think about Correlation?
#34I don’t understand any of the responses I’m reading. The question isn’t asking for an intuitive understanding of correlation. He’s just complaining that only normalized values are presented.
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Re: How to Think about Correlation?
#35Earlier quoted context omitted.
I don't quite like this answer, because it simplifies a lot of things about correlations which are just not really accurate. > Corrleations are meaningful because they indicate how strongly variables can predict other variables. This is not wrong per se, but may be wrongly interpreted. 1) I think it is important to stress that the reverse is not true. If a correlation is 0, it does not mean the variables are independ…
Good critiques, but I disagree with the last one. At least in practice in the sciences, correlation is frequently used to find good candidates for causation. In many scenarios, correlation is pretty much your only hope for finding a causal link between some variable and an outcome of interest.
To clarify, I'm not suggesting that correlation implies causation here (indeed, I think they take away your programmer card if you can't quickly parrot the phrase, "correlation doesn't mean causation").
From the NIST Engineer's Handbook:
"Generally, we first need to find and explore correlations and then try to establish causal relationships. It is much easier to find correlations as these are just properties of the data."
So I'm saying that correlation is often used (and misused) in an attempt to find good candidates for causation. This is how much science and engineering is practiced. If you disagree with this, you disagree with some fundamentals of how the scientific method is used (ie, hypothesis forming).
> To me correlation is more a way to reinforce a hypothesis of causality that is already suspected
It certainly can be used in this way, but that doesn't mean it's the only scientifically-valid way to use it.
Re: How to Think about Correlation?
#36Correlations are a profound part of our universe. When observing the universe, humans can never prove any facts about the universe. We can only establish correlations. Correlations between events that occur in our universe is the furthest "truth" we can establish about the universe short of a full on proof. What this means is that nothing in the physical universe can be proven. Proof is the domain of maths and logic,…
This (causation as correlation) revelation was highlighted by Hume and this and other work by him had profound influence on Kant (famously awaking him from his "dogmatic slumbers") and scientists like Darwin and Einstein - the latter obviously in a more healthy scientific age when those at the forefront of physics were not so disdainful of philosophers.
If you mean Hume's skepticism toward causation, then all I can say is that, as with all things Hume, he is highly overrated. The presuppositions that his arguments rest on aren't even accepted by most people who, to steal from Stroud, bow reverentially at his feet. For instance, most who pay homage to Hume do not accept his severe restrictions vis-a-vis causality in the realm of perception. But it is precisely this crude imagist theory of perception that Hume grounds his arguments against the knowledge of causation in.
(Which is not to dismiss your point about their being a kind of savagery and philosophical philistinism among scientists. This was certainly Feyerabend's view.)
Re: How to Think about Correlation?
#37The article's question: "Why are correlations meaningful?" Here's a simplified answer. Correlations are meaningful because they indicate how strongly variables can predict other variables, in some circumstances. This is valuable because some variables are easier to use than others. A positive correlation between two variables means they tend to move in the same direction (relative to their mean). A negative correlati…
> And it turns out that a strong positive correlation can be a good place to hunt for possible causality I don't disagree, but I have yet to see a mathematically clean definition of "causality".
That’s interesting, because causality requires time for the entropy engine to move our reality forward.
It’s not clear to me whether mathematical axioms would be outside of entropy driven time, or if the mere presence of operators in sequence requires entropy change to transmit the information and move the calculation forward.
Re: How to Think about Correlation?
#38Earlier quoted context omitted.
Can you expand a little further? I don't see the adjunction (between what categories?)
It's somewhat weird to see someone immediately jump to category theory when it's more likely to be about basic linear algebra. That said convolution and correlation are not linear operators but bilinear operators, so I'm struggling a bit to see in what sense they're adjoint. Maybe something like: = which does actually work if you let the inner product be the integral of the product and the correlation the time-correl…
That is what I was referring to yes, however it is also adjoints in the category theory sense.
http://www.reproducibility.org/RSF/book/bei/conj/paper_html/...
Re: How to Think about Correlation?
#39Earlier quoted context omitted.
This (causation as correlation) revelation was highlighted by Hume and this and other work by him had profound influence on Kant (famously awaking him from his "dogmatic slumbers") and scientists like Darwin and Einstein - the latter obviously in a more healthy scientific age when those at the forefront of physics were not so disdainful of philosophers.
If you mean Hume's skepticism toward causation, then all I can say is that, as with all things Hume, he is highly overrated. The presuppositions that his arguments rest on aren't even accepted by most people who, to steal from Stroud, bow reverentially at his feet. For instance, most who pay homage to Hume do not accept his severe restrictions vis-a-vis causality in the realm of perception. But it is precisely this c…
I don't have time to delve into this (delving would be required as I don't have the knowledge on tap) and respond to it, but have upvoted anyway; whether I agree or disagree with this or some of your other comments, your eloquence is appreciated!
Re: How to Think about Correlation?
#40Imagine my surprise when I realized that correlation and synchrony are (almost) the same thing.
What do you mean by synchrony?