A large class of problems in machine learning rely on Bayesian estimation of
complex parameter dependencies which can be derived from invariant
distributions of associated stochastic differential equations. These methods
are closely related to techniques used for sampling molecular systems.
Stochastic gradient methods, in which the gradient evaluation depends on a
subsampling of the available data, can significantly reduce the computational
cost, but the subsampling corrupts the gradient structure and introduces
substantial errors in the associated probability distributions for parameters.
I will describe the design of ``thermostatic'' controls and effective numerical
methods for accurate recovery of the parameter distribution in the presence of 
severe subsampling error.