  In this paper I propose a generative model of supervised learning that
unifies two approaches to supervised learning, using a concept of a correct
loss function. Addressing two measurability problems, which have been ignored
in statistical learning theory, I propose to use convergence in outer
probability to characterize the consistency of a learning algorithm. Building
upon these results, I extend a result due to Cucker-Smale, which addresses the
learnability of a regression model, to the setting of a conditional probability
estimation problem. Additionally, I present a variant of Vapnik-Stefanuyk's
regularization method for solving stochastic ill-posed problems, and using it
to prove the generalizability of overparameterized supervised learning models.
