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Causality Lab at CMU
This is very cool if you're interested in causal models.
I want to define a "supports" relation.
Given
d : Data
H : Hypothesis
We define a relation |= (read "SUPPORTS") as
d |= H iff H explains d
First Refinement:
what gets explained by a hypothesis is not the data itself, but a particular property of it. For example, when you have a data set with the variables (TV-watching-frequency, Obesity), what we wish to explain is the positive correlation between the two variables. Of course, causal models do not necessarily provide a mechanism.
So back to our definition of "SUPPORTS":
d |= H iff there exists a property P of datasets of this type such that H explains P(d)
i.e. exists P : Property(d) (H explains P(d)) #note that P is not a predicate. Predicates are of type A -> t for some A (t is the type which can only take values in {true, false}).
Although, of course, we want to generalize this to degrees. If we want to be able to do inference to the best explanation (explanations corresponding to causal models here), we would choose the model with most explanatory power... However, it might be a good idea to incorporate Occam's razor here.
This is very cool if you're interested in causal models.
I want to define a "supports" relation.
Given
d : Data
H : Hypothesis
We define a relation |= (read "SUPPORTS") as
d |= H iff H explains d
First Refinement:
what gets explained by a hypothesis is not the data itself, but a particular property of it. For example, when you have a data set with the variables (TV-watching-frequency, Obesity), what we wish to explain is the positive correlation between the two variables. Of course, causal models do not necessarily provide a mechanism.
So back to our definition of "SUPPORTS":
d |= H iff there exists a property P of datasets of this type such that H explains P(d)
i.e. exists P : Property(d) (H explains P(d)) #note that P is not a predicate. Predicates are of type A -> t for some A (t is the type which can only take values in {true, false}).
Although, of course, we want to generalize this to degrees. If we want to be able to do inference to the best explanation (explanations corresponding to causal models here), we would choose the model with most explanatory power... However, it might be a good idea to incorporate Occam's razor here.
