Ross GaylerSome probability/maths/optimisation questions for the Fedi-hive mind:
Bayes' Theorem is
P(H | E) = P(E | H) P(H) / P(E)
where H and E are events (that I have labelled for my mnemonic convenience to suggest Hypothesis and Evidence, but they're just events).
Assume that:
* There is some fixed database of records with a fixed set of fields.
* The events H and E are predicates of individual database records.
* The event predicates are functions of the field values in the record being evaluated.
* We are interpreting the relative frequency of the event predicate being true over all the record in the database as the probability of the event defined by the predicate.
The typical statement of Bayes' Theorem appears to assume that the definitions of the events H and E are fixed and given, and the only thing of interest is how to calculate with them.
1. Does it make sense to have a fixed definition of H and search over the space of possible definitions of E to maximise P(H | E)?
2. Is there a name for this? (I presume it's been suggested many times already.) Is it abductive inference because you're trying to find the "best explanation" of H?
3. Are there constraints that need to be placed on the optimisation? (a. You wouldn't want the E definition to be a copy of or equivalent to the H definition. b. You wouldn't want the E definition to be some degenerate case, e.g. with P(E) vanishingly small. c. You probably want some regularisation penalty that prefers simple definitions of E over more complex ones.
Any comments on this and pointers into the literature would be greatly appreciated.
Jon Awbrey