Generalisation

there is exactly one theorem in machine learning that every practitioner rederives on a whiteboard at least once a year, and this is it. 𐃏 the squared-error risk of any learned predictor splits into three non-negative pieces — irreducible noise, squared bias, and variance — and every design decision you make (model class, regularisation strength, \(k\), ensemble size, early stopping) is secretly a transaction between the last two.

averaged over all possible problems, every learning algorithm is exactly as good as random guessing — and every optimiser is exactly as good as blind enumeration. 𐃏 this sounds like nihilism but is actually the sharpest possible argument for inductive bias: an algorithm can only beat chance on some problems by losing to chance on others, so the whole game of machine learning is choosing whose lunch to eat.