A New Optimized Stochastic Approach for Multidimensional Integrals in Machine Learning

Stochastic techniques have been developed over many years in a range of different fields, but have only recently been applied to the problems in machine learning. A fundamental problem in this area is the accurate evaluation of multidimensional integrals. An introduction to the theory of the stochastic optimal generating vectors has been given. A new optimized lattice sequence with a special choice of the optimal generating vector has been applied to compute multidimensional integrals up to 30-dimensions. Clearly, the progress in the area of machine learning is closely related to the progress in reliable algorithms for multidimensional integration.