Researchers from Nanyang Technological University and the University of Warwick are exploring the application of possibility theory in machine learning to address limitations in probabilistic models, such as hallucinations. Unlike probability theory, which relies on strict distribution constraints, possibility theory distinguishes between aleatory and epistemic uncertainty.
In 2025, researchers introduced a possibility-theory analogue to the Donsker-Varadhan formula, which is used in machine learning to bound overfitting. This approach allows for a partial ordering of possibility functions, as it lacks the rigid requirement that the distribution density must integrate to one.
The team developed the upper CBO Optimization (uCBOpt) algorithm, an adaptation of gradient descent for possibility theory. This method incorporates weight decay directly into the update process to improve regularization control. Testing on datasets like CIFAR-10 and CIFAR-100 showed that uCBOpt-adapt performs competitively with traditional probabilistic methods.
Metrics used for evaluation included accuracy, negative log-likelihood, expected calibration error, and area under the precision-recall curve. The results indicate that possibility theory effectively manages uncertainty when information is available, providing a viable alternative to standard probabilistic frameworks in machine learning.
