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For anyone interested in this book, I'm going through it now but it addresses an important question of how to identify causality.

We've all become familiar with the refrain 'correlation does not imply causation'. This book attempts to answer: 'what DOES imply causation'? He introduces a framework for how one can answer this question. Not very mathematically rigorous, but following through the framework does appear to be able to discover non-intuitive causative conclusions.

Understanding causation will have important implications for the advancement of A.I. Finding a correlation with the causes hidden in a black box (current state of deep learning) isn't enough for many disciplines. Doctors for example will likely need to know WHY an algorithm made a decision, instead of simply running correlations and telling the operator that a patient has 80% chance of some diagnosis.

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It's possible to infer causation from correlation without experiments if you add some general assumptions.

One trick in causal discovery is additive noise. If X and Y are noisy correlating variables and X is causing Y, assumption that the noise in X is present in Y but not vice versa may reveal the direction of the causal arrow.

Causal Discovery with Continuous Additive Noise Models http://jmlr.org/papers/volume15/peters14a/peters14a.pdf

Nonlinear causal discovery with additive noise models https://papers.nips.cc/paper/3548-nonlinear-causal-discovery...

Humans seem to have causal reasoning ability that is very ad hoc. It works well in practice but it's not principled. There is not enough time to do experiments to establish facts. Correlation is causality seems to be a good heuristics.

I think that that AI will eventually learn to build causal models in the same way. Build a quick and dirty causal models with unfounded assumptions and see what works. Hold multiple effective conflicting causal theories that apply in different situations without any consistent model.

I feel like I don't have the background to fully understand what you're saying. Could you explain this in a more lay way?

> X and Y are noisy correlating variables

On average, events X and Y are positively correlated if they usually occur together even though occasionally they do not. This lack of perfect correlation is due to A) the natural variation of other (less important) causal factors, or B) imprecise measurement of their values. A and B are also known as 'noise'.

All causation implies temporal separation -- causal event X occurs before caused event Y. The trick is to identify which occurred first AND changed the frequency of the second.

An example is the assertion: "The presence of rain causes people to carry an umbrella". Of course, people carry umbrellas even when it doesn't rain, or don't carry umbrellas when it does rain, but on average, on a day when more people carry umbrellas than usual, it's usually a rainy day. The scientific question is: does people carrying umbrellas cause rain? Or does rain cause people to carry umbrellas?

If the natural variation of rain occurs in some detectable manner (e.g. light rain vs heavy rain) and you see direct variation in how people carry umbrellas (less rain thus fewer umbrellas), then it's more likely that rain causes umbrellas because rain variation correlates positively with umbrella variation. This is effectively confirmed if on several days you see that more people are carrying umbrellas than usual but it's NOT raining harder, then probably carrying of umbrellas does not cause it to rain. (Maybe umbrellas were being given away for free on that day, or the weather forecast threatened more rain than actually arrived, causing more umbrellas to be carried.)

Thus when rain amount rises or falls (due to natural variation or noise), you should see the amount of umbrella carrying follow accordingly. However if the reverse relationship occurs less often or not at all, this implies that rain does indeed cause umbrellas, and not the reverse.

Wouldnt that line of argument lead to believing that drop in barometer readings cause storms ?

If you disregard noise/variation as an indicator of which event is cause or effect, then neither of the events you propose is clearly the cause of the other. Because variation in barometer pressure is likely to be perfectly correlated with variation in storms, there's no noise/variation in either event that isn't also present in the other, so neither emerges as more likely to be the cause of the other.

This strategy of identifying the causal event works only for pairs of positively correlated events whose variations/noise sometimes do not occur together, like an increase in umbrellas without an increase in rain.

Can barometric pressure rise or fall due to causes other than storms? Can storms arise without being caused by a rise in pressure? I'd say maybe yes to the first (an elevation change of the meter, or a storm front that passes you very quickly but whose clouds don't pass directly overhead — maybe). But I'd say definite no to the second. If you are hit with rain from a storm, your baro pressure will drop. Thus storms cause pressure to drop, but pressure drop does not cause storms.

Well it's more that the noise may be in the data already... so you use that in lieu of randomization... since the noise is by definition random. You are assuming that the causal factor noisiness is different than the affected variable.

another neat example of how assumptions about noise and functional forms can let you do causal inference is in an exercise in "Elements of Causal Inference":

consider a linear model. The true model is Y ~ aX + ϵ, X causes Y. you want to distinguish, using observational data, from the case where Y causes X.

if the noise ϵ is Gaussian, there's no way to do this: there are reasonable models going both directions.

if you assume ϵ is uniformly distributed on some interval instead, then it becomes really obvious which way is the correct way.

the exercise recommends drawing little pictures with error bars to convince yourself of this, which is worth doing.

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