Computation of Conditional Expectations with Guarantees

Abstract Theoretically, the conditional expectation of a square-integrable random variable Y given d -dimensional vector X can be obtained by minimizing mean squared distance between and f ( ) over all Borel measurable functions $$f :\mathbb {R}^d \rightarrow \mathbb {R}$$ f : R d → . However, in many applications this minimization problem cannot solved exactly, instead, numerical method which computes an approximate minimum suitable subfamily has to used. The quality result depends on adequacy performance method. In paper, we derive expected value representation minimal efficiently approximated with standard Monte Carlo average. This enables us provide guarantees for accuracy any approximation expectation. We illustrate assessing expectations linear, polynomial neural network regression different concrete examples.