Ultrafast Monte Carlo for Kernel Estimators and Generalized Statistical Summations
Machine learning contains many computational bottlenecks in the form of nested summations over datasets. Kernel estimators and other methods are burdened by these expensive computations. The authors present a multi-stage stratified Monte Carlo method for approximating such summations with probabilistic relative error control. The essential idea is fast approximation by sampling in trees. This method differs from many previous scalability techniques (such as standard multi-tree methods) in that its error is stochastic, but they derive conditions for error control and demonstrate that they work.