Predicting Cause-Effect Relationships from Incomplete Discrete Observations

We address a prediction problem that frequently occurs in practice We wish to predict the value of a function on the basis of discrete obser vational dat a that are incomplete in two senses Only certain arguments of the function ar e observed and the function value is observed only for certain combinations of values of these arguments We solve the problem under a monotonicity condition that is natural in many applications and we discuss applications t o tax auditing medicine and real estate valu ation In particular we display a special class of problems for which the best mono tone prediction can be found in polynomial time