“Most of the causal inference community” agrees that causal models are made up of potential outcomes, which on the unit level are propositional logical variables that determine how some “unit” (person, etc.) responds in a particular way (Y) to a hypothetical intervention on the direct causes of Y.
Is Y a particular way of responding (e.g. Y = “the person dies”), or is it a variable that denotes whether the person responds in that way (e.g. Y=1 if the person dies and 0 otherwise)? I think you meant the latter.
If we don’t know which unit we are talking about, we average over them to get a random variable Y(pa(Y)).
How does averaging over propositional logical variables give you a random variable? I am afraid I am getting confused by your terminology.
I think it’s fine if you want to advocate a “new view” on things. I am just worried that you might be suffering from a standard LW disease of trying to be novel without adequately understanding the state of play, and why the state of play is the way it is.
I wasn’t trying to be novel for the sake of it. Rather, I was just trying to write down my thoughts on the subject. As I said before, if you have some specific pointers to the state of the art in this field, then that would be much appreciated. Note that I have a background in computer science and machine learning, so I am somewhat familiar with causal models
and moreover the only way to give the right answer to these kinds of questions is to be isomorphic to the “CDT algorithm” for these kinds of questions.
That sounds interesting. Do you have a link to a proof of this statement?
Is Y a particular way of responding (e.g. Y = “the person dies”), or is it a variable that denotes whether the
person responds in that way (e.g. Y=1 if the person dies and 0 otherwise)? I think you meant the latter.
The latter.
How does averaging over propositional logical variables give you a random variable? I am afraid I am getting
confused by your terminology.
There is uncertainty about which unit u we are talking about (given by some p(u) we do not see). So instead of a propositional variable assignment Y(pa(y), u) = y, we have an event with a probability p{ Y(pa(y)) = y } = \sum{u : Y(pa(y),u) = y } p(u).
That sounds interesting. Do you have a link to a proof of this statement?
I am not sure I made a formal enough statement to prove. I guess:
(a) if you believe that your domain is acyclic causal, and
(b) you know what the causal structure is, and
(c) your utility is a function of the outcomes sitting in your causal system, and
(d) your actions on a variable embedded in your causal system break causal links operating from usual direct causes to the variable, and
(e) your domain isn’t “crazy” enough to demand adjustments along the lines of TDT,
then the right thing to do is to use CDT.
These preconditions hold in the HAART example. I am not sure exactly how to formalize (e) (I am not sure anyone does, this is a part of what is open).
Is Y a particular way of responding (e.g. Y = “the person dies”), or is it a variable that denotes whether the person responds in that way (e.g. Y=1 if the person dies and 0 otherwise)? I think you meant the latter.
How does averaging over propositional logical variables give you a random variable? I am afraid I am getting confused by your terminology.
I wasn’t trying to be novel for the sake of it. Rather, I was just trying to write down my thoughts on the subject. As I said before, if you have some specific pointers to the state of the art in this field, then that would be much appreciated. Note that I have a background in computer science and machine learning, so I am somewhat familiar with causal models
That sounds interesting. Do you have a link to a proof of this statement?
The latter.
There is uncertainty about which unit u we are talking about (given by some p(u) we do not see). So instead of a propositional variable assignment Y(pa(y), u) = y, we have an event with a probability p{ Y(pa(y)) = y } = \sum{u : Y(pa(y),u) = y } p(u).
I am not sure I made a formal enough statement to prove. I guess:
(a) if you believe that your domain is acyclic causal, and
(b) you know what the causal structure is, and
(c) your utility is a function of the outcomes sitting in your causal system, and
(d) your actions on a variable embedded in your causal system break causal links operating from usual direct causes to the variable, and
(e) your domain isn’t “crazy” enough to demand adjustments along the lines of TDT,
then the right thing to do is to use CDT.
These preconditions hold in the HAART example. I am not sure exactly how to formalize (e) (I am not sure anyone does, this is a part of what is open).