The Three Layer Causal Hierarchy [pdf]
web.cs.ucla.edu
web.cs.ucla.edu
Rain causes people to be wet. This implies that if we were to God-like stop the rain, people wouldn't be wet. But if we were to prevent people from being wet (by buying them an umbrella), that wouldn't stop the rain. This is not something you can infer from correlations alone.
There's plenty of reason to believe that causal relationships are structural simplifications of correlative ones. We just don't have any great formalizations of them.
Like if I say "blue", you can very quickly simplify by assuming I'm talking about the color blue, rather than all the other things in the world that are also called 'blue', even though there's nothing that necessitates this simplification.
Yes, I agree. Just like linear models are a specific subset of quadratic models.
than the features of correlative relations that do not take part in causal structure.
In my mind, causality is an additional set of modeling assumptions that greatly enhance our ability to do logical and probabilistic inference.
By the way, this is not true in general. Suppose B…F are sampled from Boolean variables with bias 0.5. A Boolean circuit like A = (sum(B,C,D,E,F)>3) + (not B and not C and… not F). A is correlated with all of its causes B through F. However, stopping all of its causes, causes A to turn on.
> If you were to stop all of those things, you could surely stop the rain as well.
But, you typically can't intervene everywhere. For example, you may not have any power over the gardener who normally turns the sprinkler on. The point of interventions (like turning a sprinkler on) is that you can reason about what would happen.
Let's look at a concrete example. Suppose in the real world, the gardener leaves the sprinkler off, the ground is dry.
If you were to observe that the sprinkler is on, you would deduce that the ground is wet. If you were to observe the wet ground, you would "abduce" that the sprinkler is on.
However, the interventional question: what if I were to turn on the sprinkler requires a causal model. In this case, the direction is critical. Turning on the sprinkler, wets the ground. Wetting the ground, does not turn on the sprinkler!
Causal models also have better invariants: unobserved causal children (say WetGround) leave their parents (say Sprinkler and Rain) independent. This is not necessarily true in an associational model. If Rain is correlated with WetGround is correlated with Sprinkler, then even when WetGround is unobserved, Rain gives you information about Sprinkler. Since our model has no other elements (such as a common cause between Sprinkler and Rain), then this transmission of information is totally wrong.
I couldn't tell if you were arguing against the utility of causal models or whether the real world exhibits causal relationships. If it's the latter, then it is ultimately a leap of faith based on our intuitive understanding of the world. All scientific experiments rely on the notion of cause and effect and interventional reasoning (experiments).