Engines of Evidence – A Conversation with Judea Pearl
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If Correlation Doesn’t Imply Causation, then What Does? http://www.michaelnielsen.org/ddi/if-correlation-doesnt-impl...
I read this myself few years ago, got very excited, and had a go at writing a program that could automatically perform the derivation from Nielsen's worked example:
https://github.com/fcostin/d_separation
This was really interesting to work on, but I guess I became disinterested in it after I got it to crudely work. Be aware that the quality of the code, documentation, and the entire idea of the "proof-search" aspect of it is probably not very good.
http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_model...
My personal opinion is that it is a very good book, just a bit hard.
It is incredible bit of research, I agree, but it still has rough edges and should be treated as such, a work in progress. I do not think this book should be the bible of causality, and I think we're worse off for thinking it is.
Personally, I find the work of Richardson and Robins in Single World Intervention Graphs https://www.csss.washington.edu/Papers/wp128.pdf far more intuitive and compelling than Pearl's do-calculus. The notation is too slightly cleaner and it does away mostly with the unorthodox notation Pearl uses.
In addition to presenting Pearl's ideas more clearly than Pearl himself tends to do, Morgan and Winship also describe Rubin's work more fairly than Pearl does. (On the other hand, Rubin also tends to disparage Pearl's work more than is necessary.)
The do-calculus to me looks a bit cumbersome. I'm not generally attracted to math that doesn't look like math, except if it is nice looking. :-)
On a more general level, when I'm building robots, I consider the interface between their minds and the world a Markov blanket. This means that state in the world can only be represented in the robot by learning through its interface by a combination of forward and inverse models. The existence of a physical barrier makes it possible to define information going through it. You might suggest that the world is created by the robot's mind, but that is probably difficult to back with any information criterion.
If the robot learns its body, it knows that it is itself who is performing a movement or if it is being pushed. Knowing that it was itself the actor is enough to know the direction of the causal arrow.
I'm not sure if that's gonna be the final title though.
https://www.amazon.com/Causal-Inference-Statistics-Judea-Pea...
But I couldn't help thinking that the presentation could be improved a little. I am not clever enough to figure out how; it's just a feeling I have.
I recommend starting with the less wrong articles linked here. Eliezer Yudkowdky is great at explaining things.
The way it was done in the book required some tricks. And the way the tricks worked was to make assumptions about how the causality flowed, and that the model captured all possible causes of an effect. For example, with the "does smoking causes lung cancer" example (back propagation), you had to say that smoking causes tar in the lungs, which is the only possible source of lunch cancer. (this might not be exactly right, my memory is a bit hazy now). I'd be happy to hear from someone who is more of an expert than I am.
I am on a train so I can't do more than refer to http://lesswrong.com/lw/ev3/causal_diagrams_and_causal_model... unfortunately.
I enjoyed Probabilistic Reasoning in Intelligent systems. I was unaware of Causality.
Pearl's theory summarized in chapter 5, but it is put into context: related work, criticism, etc...