A New Perspective on Machine Learning: How to do Perfect Supervised Learning
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In this work, we introduce the concept of bandlimiting into the theory of machine learning because all physical processes are bandlimited by nature, including real-world machine learning tasks. After the bandlimiting constraint is taken into account, our theoretical analysis has shown that all practical machine learning tasks are asymptotically solvable in a perfect sense. Furthermore, the key towards this solvability almost solely relies on two factors: i) a sufficiently large amount of training samples beyond a threshold determined by a difficulty measurement of the underlying task; ii) a sufficiently complex model that is properly bandlimited. Moreover, for unimodal data distributions, we have derived a new error bound for perfect learning, which can quantify the difficulty of learning. This case-specific bound is much tighter than the uniform bounds in conventional learning theory.
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