We examine a probabilistic model for the diagnosis of multiple diseases. In the model, diseases and findings are represented as binary variables. Also, diseases are marginally inde pendent, features are conditionally independent given disease instances, and diseases interact to produce findings via a noisy OR-gate. An algorithm for computing the posterior probability of each disease, given a set of observed findings, called quickscore,  One of the most common criticisms of the use of probability theory in expert-system applications is that the theory is impractical to apply in realistic situations [1] . In attempts to answer this criticism, several researchers at Stanford, myself included, have undertaken the task of converting to a probabilistic framework Quick Medical Reference (QMR) [10] , one of the largest medical expert systems in existence. We have made a straightforward and tractable tranformation of the QMR knowledge base to a probabilisitc model [6, 8). Like the heuristic algorithms in QMR, the model allows for any combination of diseases to be present in a patient. Unfortunately, this feature leads to a time complexity for inferring the probability of each disease given a set of findings that is exponential in the number of diseases (0(2n)) for all known algorithms. As there are over 600 diseases in QMR, these algorithms are intractable. Furthermore, this problem is known to be NP-hard [2] . In this paper, I present quickscore, an algorithm with time complexity that is exponential in the number of positive findings. More precisely, the algorithm has a time complexity of O(nm-2m + ), where m+ is the number of positive findings and m-is the number of negative findings. Although quickscore has an exponential time complexity, it is useful in practice because the number of observed positive findings is often far less than the number of diseases under consideration. For many realistic patient cases, quickscore implemented on a Macintosh II produces an answer in less than 1 minute of real time.
The Quickscore formulation by REF takes advantage of the noisy-or parameterization to give an exact inference algorithm that is polynomial in the number of negative findings but still exponential in the number of positive findings.
A Tractable Inference Algorithm for Diagnosing Multiple Diseases
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Computer Science