1 research outputs found
Computation of conditional expectations with guarantees
Theoretically, the conditional expectation of a square-integrable random
variable given a -dimensional random vector can be obtained by
minimizing the mean squared distance between and over all Borel
measurable functions . However, in many
applications this minimization problem cannot be solved exactly, and instead, a
numerical method that computes an approximate minimum over a suitable subfamily
of Borel functions has to be used. The quality of the result depends on the
adequacy of the subfamily and the performance of the numerical method. In this
paper, we derive an expected value representation of the minimal mean square
distance which in many applications can efficiently be approximated with a
standard Monte Carlo average. This enables us to provide guarantees for the
accuracy of any numerical approximation of a given conditional expectation. We
illustrate the method by assessing the quality of approximate conditional
expectations obtained by linear, polynomial as well as neural network
regression in different concrete examples