Universal Operator Induction with partial operators

[Nil Geisweiller]

Hi,

do you know any work regarding Operator Induction, as defined in [1],
involving complete and partial operators? A complete operator
calculates a conditional distribution over answers given any question,
while a partial operator calculates a conditional distribution over
answers given a subset of questions only. It could be written as

O_partial(A|Q) = if property(Q) then calculate_prob(Q, A)

The hard part of course is to combine operators that are both complete
and partial, or partial over different subsets of questions, when
trying to maximize the fitness.

I can see that considering a partial operator as a class of complete
operators of the form

if propety(Q) then calculate_prob(Q, A) else <anything>

brings us back to good old Universal Operator Induction. In practice
however I wonder if there are better ways.

Let me know if you want more details, obviously a google search didn't
yield anything, so I very much welcome your help.

Nil

[1] Three Kinds of Probabilistic Induction: Universal Distributions
and Convergence Theorems. Ray Solomonoff.

[Eray Ozkural]

There are no obvious answers to that question I suppose. It's really just a very general formulation of the problem, and as such doesn't explain how any of the computations are to be done. It's still good to know that something like that could work, of course. :)

Best Wishes,

Eray

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[Nil Geisweiller]

Thanks Eray, I appreciate.

Out of a better plan for now, I'll try to approximate the class
corresponding to a partial model by a fictive model that perfectly
explains the remaining data (undefined in the partial model), because
it's likely the dominant one, and estimate its length by a function of
the length of the unexplained data.

Nil

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[Eray Ozkural]

Every researcher here should really try to understand current applications of the information bottleneck method. Best theoretical discussion of fictive variables in the literature that I can think of.

Best,

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Eray Ozkural, PhD. Computer Scientist
Founder, Gok Us Sibernetik Ar&Ge Ltd.
http://log.examachine.net
http://github.com/examachine http://groups.yahoo.com/group/ai-philosophy

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