Predicting Cause-Effect Relationships from Incomplete Discrete Observations

This paper addresses a prediction problem occurring frequently in practice. The problem consists in predicting the value of a function on the basis of discrete observational data that are incomplete in two senses. Only certain arguments of the function are observed, and the function value is observed only for certain combinations of values of these arguments. The problem is considered under a monotonicity condition that is natural in many applications. Applications to tax auditing, medicine, and real estate valuation are discussed. In particular, a special class of problems is identified for which the best monotone prediction can be found in polynomial time