In the first counterexample you describe the desired behavior as
Intuitively, we expect each node in the human Bayes net to correspond to a function of the predictor’s Bayes net. We’d want the reporter to simply apply the relevant functions from subsets of nodes in the predictor’s Bayes net to each node in the human Bayes net [...]
After applying these functions, the reporter can answer questions using whatever subset of nodes the human would have used to answer that question.
Why doesn’t the reporter skip the step of mapping the predictor’s Bayes net to the human’s and instead just answer the question using its own nodes? What’s the benefit of having the intermediate step that maps the predictor’s net to the human’s?
We generally imagine that it’s impossible to map the predictors net directly to an answer because the predictor is thinking in terms of different concepts, so it has to map to the humans nodes first in order to answer human questions about diamonds and such.
I see, thanks for answering. To further clarify, given the reporter’s only access to the human’s nodes is through the human’s answers, would it be equally likely for the reporter to create a mapping to some other Bayes net that is similarly consistent with the answers provided? Is there a reason why the reporter would map to the human’s Bayes net in particular?
The dataset is generated with the human bayes net, so it’s sufficient to map to the human bayes net. There is, of course, an infinite set of “human” simulators that use slightly different bayes nets that give the same answers on the training set.
Potentially silly question:
In the first counterexample you describe the desired behavior as
Why doesn’t the reporter skip the step of mapping the predictor’s Bayes net to the human’s and instead just answer the question using its own nodes? What’s the benefit of having the intermediate step that maps the predictor’s net to the human’s?
We generally imagine that it’s impossible to map the predictors net directly to an answer because the predictor is thinking in terms of different concepts, so it has to map to the humans nodes first in order to answer human questions about diamonds and such.
I see, thanks for answering. To further clarify, given the reporter’s only access to the human’s nodes is through the human’s answers, would it be equally likely for the reporter to create a mapping to some other Bayes net that is similarly consistent with the answers provided? Is there a reason why the reporter would map to the human’s Bayes net in particular?
The dataset is generated with the human bayes net, so it’s sufficient to map to the human bayes net. There is, of course, an infinite set of “human” simulators that use slightly different bayes nets that give the same answers on the training set.