A method for predicting sensor output values of a machine sensor monitoring system includes providing a set of input sensor data X and a set of output sensor data Y for a plurality of sensors the monitor the performance of a machine, learning a functional relationship that maps the input sensor data to the output sensor data by maximizing a logarithm of a marginalized conditional probability function P(Y|X) where a dependence of the output sensor data Y with respect to unknown hidden machine inputs u has been marginalized, providing another set of input sensor data X′, and calculating expected values of the output sensor data Y′ using the input sensor data X′ and the marginalized conditional probability function P(Y|X′), where the calculated expectation values reflect the dependence of the output sensor data Y″ with respect to the unknown hidden machine inputs u.