We critically review three major theories of machine learning and provide a new theory according to which machines learn a function when the machines successfully compute it. We show that this theory challenges common assumptions in the statistical and the computational learning theories, for it implies that learning true probabilities is equivalent neither to obtaining a correct calculation of the true probabilities nor to obtaining an almost-sure convergence to them. We also briefly discuss some case studies from natural language processing and macroeconomics from the perspective of the new theory.

翻译：本文批判性地回顾了机器学习的三大主要理论，并提出了一种新理论：当机器成功计算出一个函数时，即实现了对该函数的学习。我们证明该理论对统计学习理论与计算学习理论中的常见假设提出了挑战，因为它意味着学习真实概率既不等同于获得对真实概率的正确计算，也不等同于获得几乎必然收敛于真实概率的结果。最后，我们基于新理论的视角简要讨论了自然语言处理与宏观经济学中的若干案例研究。