We provide a new representation-independent formulation of Occam's razor theorem, based on Kolmogorov complexity. This new formulation allows us to: (i) Obtain better sample complexity than both length-based and VC-based versions of Occam's razor theorem, in many applications. (ii) Achieve a sharper reverse of Occam's razor theorem than previous work. Specifically, we weaken the assumptions made in an earlier publication, and extend the reverse to superpolynomial running times.
Categories: cs.LG cond-mat.dis-nn cs.AI cs.CC math.PR physics.data-an