Correlation, Causation, and Confusion

http://www.thenewatlantis.com/publications/correlation-causation-and-confusion

by gwern • 11 years ago

48 6 11 years ago

thenewatlantis.com

markcmyers• 11 years ago

This is a masterpiece.

le0n2• 11 years ago

+1. A fantastic article. Definitely one of the best popular-level stats pieces I've read.

zero-rated• 11 years ago

The New Atlantis is one to keep an eye on. The articles are deeper and more insightful than most. It makes the Economist look downright shallow in comparison.

Houshalter• 11 years ago

I think the statistics used in a lot of actual science are too primitive. Not that the methods are simple or old by any means. Or that making them more complicated is desirable in itself. Just that there are better ways of inferring structure from data.

Just correlating two variables will often be misleading. E.g. the coffee drinkers that live longer. But if you collect a ton of other information, you will find many other relevant variables. And once you build a model from all that information, you find that coffee no longer predicts mortality.

Of course there is a limit to the amount of causal structure you can infer from data. But that limit is well above what we are currently doing. And the more relevant data you collect, the higher that limit is.

This is basically what the field of machine learning is. Where we want computers to automatically model our data and make the most accurate predictions for us. Tons of methods are invented and tested against each other on different datasets. There are websites like kaggle where users compete to find the best model for a dataset. But somehow none of this innovation goes back to mainstream statistics or used in scientific studies to get better models.

And machine learning sucks too. A lot of methods use maximum likelihood with some tricks to keep it from overfitting. Rather than ideal bayesian methods. And the models are kind of simple. Like simple decision trees or linear models.

I think in the future we will use something like bayesian neural networks. Which can model very complicated structures with little data. And we won't arbitrarily select some of the variables to be inputs and some to be outputs. All of the observed variables are outputs of some unobserved function with unobserved inputs. We need to model that.

Then you have a fully general statistics algorithm that you can plug any dataset into. You can then ask it questions like "if I observed that this person drank coffee, but everything else I know about them is the same, what is their mortality?" And then it will give you the most accurate possible answer.

Is that proof of causation? No. But it's far more likely that coffee causes cancer if it can accurately predict it, even when you control for all other variables. Than if you just see that it happens to correlate with cancer.

le0n2• 11 years ago

I don't think machine learning vs Bayes vs sampling theory has much to do with the content of the article, which is more about causality than interpretations of probability.

it's far more likely that coffee causes cancer if it can accurately predict it, even when you control for all other variables

I don't know about this: prediction is not equivalent to explanation in general. The "all the other variables" bit is also a bit of a kicker (what counts as "all"?) -- hence randomization, and, well, pretty much everything else the article discusses.

mizzao• 11 years ago

As someone who studies causality via experiments for a living, this article is a remarkably accessible synthesis given that it covers so much from different disciplines.

Definitely bookmarked as a juicy morsel to send to anyone who asks, "why should we care about causality?"

Correlation, Causation, and Confusion

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