...that was written by a Less Wrong reader. Or if not, someone who independently reinvented things to well past the point where I want to talk to them. Do you know the author?
Hasn’t using DAGs to talk about causality long been a staple of the philosophy and computer science of causation? The logical positivist philosopher Hans Reichenbach used directed acyclic graphs to depict causal relationships between events in his book The Direction of Time (1956). (See, e.g., p. 37.)
A little searching online also turned up this 1977 article in Proc Annu Symp Comput Appl Med Care. From p. 72:
When a set of cause and effect relationships between states is specified, the resulting structure is a network, or directed acyclic graph of states.
That article came out around the time of Pearl’s first papers, and it doesn’t cite him. Had his ideas already reached that level of saturation?
ETA: I’ve looked a little more closely at the 1977 paper, which is entitled “Problems in the Design of Knowledge Bases for Medical Consultation”. It appears to completely lack the idea of performing surgery on the DAGs, though I may have missed something. Here is a longer quote from the paper (p. 72):
Many states may occur simultaneously in any disease process. A state thus defined may be viewed as a qualitative restriction on a state variable as used in control systems theory. It does not correspond to one of the mutually exclusive states that could be used to describe a probabilistic system.
[...]
When a set of cause and effect relationships between states is specified, the resulting structure is a network, or directed acyclic graph of states.
The mappings between nodes n_i of the causal net are of n_i—a_{ij} --> n_j where a_{ij} is the strength of causation (interpreted in terms of its frequency of occurrence) and n_i and n_j are states which are summarized by English language statements. This rule is interpreted as: state n_i causes state n_j, independent of other events, with frequency a_{ij}. Starting states are also assigned a frequency measure indicating a prior or starting frequency. The levels of causation are represented by numerical values, fractions between zero and one, which correspond to qualitative ranges such as: sometimes, often, usually, or always.
So, when it comes to demystifying causation, there is still a long distance from merely using DAGs to using DAGs in the particularly insightful way that Pearl does.
This paper is remarkable not only because it correctly formalizes causation in linear models using DAGs, but also that it gives a method for connecting causal and observational quantities in a way that’s still in use today. (The method itself was proposed in 1923, I believe). Edit: apparently in 1920-21, with earliest known reference apparently dating back to 1918.
Using DAGs for causality certainly predates Pearl. Identifying “randomization on X” with “dividing by P(x | pa(x))” might be implicit in fairly old papers also. Again, this idea predates Pearl.
There’s always more to the story than one insightful book.
Good find, thanks. The handwritten equations are especially nice.
Ilya, it looks you’re the perfect person to write an introductory LW post about causal graphs. We don’t have any good intro to the topic showing why it is important and non-obvious (e.g. the smoking/tar/cancer example). I’m willing to read drafts, but given your credentials I think it’s not necessary :-)
The point is that it’s not commonly internalized to the point where someone will correctly use DAG as a synonym for “universe”.
Synonym? Not just ‘capable of being used to perfectly represent’, but an actual literal synonym? That’s a remarkable claim. I’m not saying I outright don’t believe it but it is something I would want to see explained in detail first.
Would reading Pearl (competently) be sufficient to make someone use the term DAG correctly in that sense?
The point is that it’s not commonly internalized to the point where someone will correctly use DAG as a synonym for “universe”.
All that I see in the quote is that the DAG is taken to determine what happens to you in some unanalyzed sense. You often hear similar statements saying that the cold equations of physics determine your fate, but the speaker is not necessarily thinking of “equations of physics” as synonymous with “universe”.
Hasn’t using DAGs to talk about causality long been a staple of the philosophy and computer science of causation? The logical positivist philosopher Hans Reichenbach used directed acyclic graphs to depict causal relationships between events in his book The Direction of Time (1956). (See, e.g., p. 37.)
A little searching online also turned up this 1977 article in Proc Annu Symp Comput Appl Med Care. From p. 72:
That article came out around the time of Pearl’s first papers, and it doesn’t cite him. Had his ideas already reached that level of saturation?
ETA: I’ve looked a little more closely at the 1977 paper, which is entitled “Problems in the Design of Knowledge Bases for Medical Consultation”. It appears to completely lack the idea of performing surgery on the DAGs, though I may have missed something. Here is a longer quote from the paper (p. 72):
So, when it comes to demystifying causation, there is still a long distance from merely using DAGs to using DAGs in the particularly insightful way that Pearl does.
Hi, you might want to consider this paper:
http://www.ssc.wisc.edu/soc/class/soc952/Wright/Wright_The%20Method%20of%20Path%20Coefficients.pdf
This paper is remarkable not only because it correctly formalizes causation in linear models using DAGs, but also that it gives a method for connecting causal and observational quantities in a way that’s still in use today. (The method itself was proposed in 1923, I believe). Edit: apparently in 1920-21, with earliest known reference apparently dating back to 1918.
Using DAGs for causality certainly predates Pearl. Identifying “randomization on X” with “dividing by P(x | pa(x))” might be implicit in fairly old papers also. Again, this idea predates Pearl.
There’s always more to the story than one insightful book.
Good find, thanks. The handwritten equations are especially nice.
Ilya, it looks you’re the perfect person to write an introductory LW post about causal graphs. We don’t have any good intro to the topic showing why it is important and non-obvious (e.g. the smoking/tar/cancer example). I’m willing to read drafts, but given your credentials I think it’s not necessary :-)
The point is that it’s not commonly internalized to the point where someone will correctly use DAG as a synonym for “universe”.
Synonym? Not just ‘capable of being used to perfectly represent’, but an actual literal synonym? That’s a remarkable claim. I’m not saying I outright don’t believe it but it is something I would want to see explained in detail first.
Would reading Pearl (competently) be sufficient to make someone use the term DAG correctly in that sense?
All that I see in the quote is that the DAG is taken to determine what happens to you in some unanalyzed sense. You often hear similar statements saying that the cold equations of physics determine your fate, but the speaker is not necessarily thinking of “equations of physics” as synonymous with “universe”.