In this paper, we consider some problems in learning with respect to a fixed distribution. We introduce two new notions of learnability; these are probably uniformly approximately correct (PUAC) learnability which is a stronger requirement than the widely studied PAC learnability, and minimal empirical risk (MER) learnability, which is a stronger requirement than the previously defined notions ...

Coalitional stability in hedonic games has usually been considered in the setting where agent preferences are fully known. We consider the setting where agent preferences are unknown; we lay the theoretical foundations for studying the interplay between coalitional stability and (PAC) learning in hedonic games. We introduce the notion of PAC stability — the equivalent of core stability under un...

We prove that log n-decision lists |the class of decision lists such that all their terms have low Kolmogorov complexity| are learnable in the simple PAC learning model. The proof is based on a transformation from an algorithm based on equivalence queries (found independently by Simon). Then we introduce the class of simple decision lists, and extend our algorithm to show that simple decision l...

We prove that strict width two branching programs or SW2 (which are width two branching programs with exactly two sinks, as defined in [BDFP86]) are properly PAC learnable under any distribution. We also observe that PAC learning monotone width two branching programs (which are width two branching programs with exactly one rejecting sink) is as hard as learning DNF formulae. This work refines b...