A new model for inductive inference

• Authors: Ronald L. Rivest;Robert Sloan
• Venue: TARK '88 Proceedings of the 2nd conference on Theoretical aspects of reasoning about knowledge
• Year: 1988

We introduce a new model for inductive inference, by combining a Bayesian approach for representing the current state of knowledge with a simple model for the computational cost of making predictions from theories. We investigate the optimization problem: how should a scientist divide his time between doing experiments and deducing predictions for promising theories. We propose an answer to this question, as a function of the relative costs of making predictions versus performing experiments. We believe our model captures many of the qualitative characteristics of "real" science. We believe that this model makes two important contributions. First, it allows us to study how a scientist might go about acquiring knowledge in a world where (as in real life) there are costs associated with both performing experiments and with computing the predictions of various theories. This model also lays the groundwork for a rigorous treatment of a machine-implementable notion of "subjective probability". Subjective probability is at the heart of probability theory [5]. Previous treatments have not been able to handle the difficulty that subjective probabilities can change as the result of "pure thinking"; our model captures this (and other effects) in a realistic manner. In addition, we begin to provide an answer to the question of how to trade-off "thinking" versus "doing"---a question that is fundamental for computers that must exist in the world and learn from their experience.