Learning from Satisfying Assignments Using Risk Minimization

In this paper we consider the problem of Learning from Satisfying Assignments introduced by \cite{1} of finding a distribution that is a close approximation to the uniform distribution over the satisfying assignments of a low complexity Boolean function $f$. In a later work \cite{2} consider the same problem but with the knowledge of some continuous distribution $D$ and the objective being to estimate $D_f$, which is $D$ restricted to the satisfying assignments of an unknown Boolean function $f$. We consider these problems from the point of view of parameter estimation techniques in statistical machine learning and prove similar results that are based on standard optimization algorithms for Risk Minimization.