Coordinates of Statistical Learning

Established results of statistical learning theory are systematised here in axiomatic form. No technical originality is claimed: the central statements reformulate known theorems. The contribution, if any, is structural: the problem is defined as the quadruple (D, F, l, A), whose three non-trivial arrows open three gaps -expressivity, induction, search- of which the central statements are a direct reading and through which the excess risk factorises. The mutual irreducibility of the gaps is proved and the relativity of their exhaustiveness is declared: the triad is canonical with respect to the adopted definition, not absolute -a weak chart, not a privileged coordinate system-. The synthesis object I = eval o A is made precise as a morphism in a Markov category. The triad is finally condensed into a single functional -the free energy F_beta-, whose minimum is the Gibbs posterior, whose gradient flow is the search dynamics, and whose bound certifies generalisation; the consistency of that form requires the fluctuation-dissipation relation and turns into a corollary, within the variational condensation adopted, the postulate of randomness. This deposit includes the English and Spanish editions