A Tractable Inference Algorithm for Diagnosing Multiple Diseases (1304.1511v2)

Abstract: 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 independent, 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, is presented. The time complexity of the algorithm is O(nm-2m+), where n is the number of diseases, m+ is the number of positive findings and m- is the number of negative findings. Although the time complexity of quickscore i5 exponential in the number of positive findings, the algorithm is useful in practice because the number of observed positive findings is usually far less than the number of diseases under consideration. Performance results for quickscore applied to a probabilistic version of Quick Medical Reference (QMR) are provided.

• The paper presents QuickScore, an algorithm that computes posterior disease probabilities using a noisy OR-gate to model interactions between diseases and findings.
• It achieves tractability by limiting exponential complexity to the typically few positive findings in clinical scenarios.
• The study highlights potential extensions, such as leaky OR-gates, to enhance diagnostic accuracy and integrate with advanced AI methods.

A Tractable Inference Algorithm for Diagnosing Multiple Diseases

The paper addresses a critical challenge in probabilistic medical diagnosis by introducing QuickScore, an algorithm tailored to compute the posterior probability of multiple diseases given a set of observations. Notably, in a typical medical diagnostic context, diseases and symptoms (findings) are represented as binary variables, with diseases being marginally independent and findings being conditionally independent given diseases. The core innovation lies in using a noisy OR-gate to model interactions between diseases and findings.

Algorithmic Complexity and Practical Viability

QuickScore presents an operational advance over previous probabilistic inference methods in medical diagnosis, with its time complexity expressed as $O(nm^{-}2^{m^{+})}$. Here $n$ represents the number of diseases, $m^{+}$ the number of positive findings, and $m^{-}$ the number of negative findings. Although exponential in the number of positive findings, this complexity is deemed practical because the number of positive findings is usually substantially smaller than the number of considered diseases. This distinction of the algorithm's scope renders it applicable in practice. Extensive simulations report that QuickScore handles typical patient cases efficiently — often providing results in under a minute with realistic numbers of positive findings.

Model Assumptions and Extensions

The paper assumes diseases are marginally independent, and findings are conditionally independent given diseases. Furthermore, causal independence is modeled via the noisy OR-gate, which posits that diseases act independently to cause any given finding. The authors acknowledge potential limitations within this framework. For instance, real-world medical data may involve multivalued disease states or causally dependent diseases and findings, aspects not directly accommodated by QuickScore.

Such assumptions, although simplifying, provide a tractable framework for probabilistic inference within Quick Medical Reference (QMR)-DT systems. Several proposed extensions, including leaky OR-gates and causal interaction modeling, could address inherent limitations, enabling richer, more nuanced representations of complex disease-finding interactions and interdependencies. Nonetheless, incorporating such extensions demands algorithmic adjustments that are presently non-trivial for the current QuickScore's framework.

Implications and Speculation on Future AI Developments

The QuickScore algorithm offers a foundational method for efficient probabilistic diagnosis in multi-disease contexts and serves as a benchmark against which newer approximation algorithms can be evaluated. It proves especially useful for verifying convergence properties in Monte-Carlo based methods and other advanced stochastic inference techniques.

Looking ahead, AI development in medical diagnostics could benefit from integrating richer causal models, potentially leveraging deep learning's capability to handle multivalued variables and complex dependencies. Advances in computational power and algorithms may facilitate the adaptation of QuickScore-like efficient methods to blend with broader AI initiatives in probabilistic reasoning and causal inference. Such progress will likely necessitate interdisciplinary collaboration, integrating knowledge from computer science, medicine, and statistics.

In conclusion, QuickScore is an instrumental step towards making probabilistic reasoning applicable in large-scale medical expert systems while laying the groundwork for future innovations in probabilistic AI methods.