In this talk we first briefly review some results obtained in analytic information theory that led to very precise asymptotics of the minimax redundancy for some universal source coding. Then we go beyond this trodden path and attempt to apply analytic tools to some machine learning problems. In particular, we present some new results on regret for online regression with logarithmic loss. These problems are analyzed using tools of analytic combinatorics such as multidimensional Fourier analysis, analytic geometry, Mellin transform, and multidimensional saddle point method.

Joint work with M. Drmota, P. Jacquet and C. Wu.