[comp.ai] Valiant's Learning Model

dario@techunix.BITNET (Dario Ringach) (11/06/88)

Is it fair to assume a constant probabilistic distribution Px on space
X during the learning process?  I mean a *good* teacher would draw
points of X so as to minimize the error between the current hypothesis
and the concept to be learnt , so that the distribution Px could
change after presenting each sample (i.e. Px(n) is now a stochastic
process).  Are these two models equivalent in the sense that they can
learn the same classes of concepts?

Has anyone attempted to approach learning as a discrete time Markov
process on the hypothesis space H?  For instance at any time k let
h1=h(k) be the current hypothesis obviously there is defined for any
h2 in H a transition probability P(h(h+1)=h2|h(k)=h1) that depends
on the probability distribution Px and the learning algorithm A.

bwk@mitre-bedford.ARPA (Barry W. Kort) (11/08/88)

In article <6083@techunix.BITNET> dario@techunix.BITNET (Dario Ringach) writes:

 > Has anyone attempted to approach learning as a discrete time Markov
 > process on the hypothesis space H?  For instance at any time k let
 > h1=h(k) be the current hypothesis obviously there is defined for any
 > h2 in H a transition probability P(h(h+1)=h2|h(k)=h1) that depends
 > on the probability distribution Px and the learning algorithm A.

Look into Bayesian inference, Kalman filtering, and Kailath's
Innovations Process.  In each of these approaches, a current
best guess is updated as new information comes in.  I believe
Widrow's adaptive networks also exhibit such behavior.

--Barry Kort