Statistical Sufficiency for Classes in Empirical L2 Spaces
Shahar Mendelson, Naftali Tishby · 2000
We explore the notion of " sufficient linear statistics for a class of real valued functions. We show that for function classes with a polynomial rate of the Parametric Pollard dimension one can find a set of linear empirical functionals of polynomial size in the dimension that are sufficient for " approximation of any function in the class. We also present a probabilistic scheme for producing those functionals.