From Non-Parametric Predictive Inference to Evidence-Theoretic Uncertainty Representation in Artificial Intelligence

Artificial intelligence systems that learn or reason from finite empirical data often require uncertainty representations that go beyond a single precise probability distribution. This is especially relevant when observations are scarce, incomplete or not reliable enough to support precise probabilistic assessments. In current data-driven AI tools, empirical information extracted from data must often be converted into a structured uncertainty model before it can be used for reasoning, learning or decision support. The singleton intervals induced by NPI-M and A-NPI-M provide such a representation, since they express the predictive information obtained from the observed data without introducing externally chosen cautiousness parameters. Evidence theory is useful in this context because it allows partial support to be assigned to sets of alternatives, making it suitable for representing imperfect knowledge in AI systems. This paper studies how Non-Parametric Predictive Inference for multinomial data (NPI-M) can be connected with evidence theory through reachable probability intervals. Since the exact NPI-M model does not directly define a credal set, we focus on its approximated version, A-NPI-M, which preserves the NPI-M singleton bounds and represents them through reachable probability intervals. We analyze whether the resulting credal set can be represented exactly by a belief function, showing that this is not possible in general, although exact representations may exist in particular cases. Motivated by this limitation, we construct a basic probability assignment whose belief and plausibility values reproduce the A-NPI-M singleton bounds. The resulting belief function preserves the marginal interval information of A-NPI-M while adding an evidential structure on composite events, and its associated set of compatible probability distributions is included in the A-NPI-M credal set. The construction is presented by cases, illustrated with numerical examples and compared with the belief-function representation of the Imprecise Dirichlet Model. The proposed model provides a theoretical representation layer that may support uncertainty-aware AI procedures by transforming empirical predictive information into structured imperfect knowledge before reasoning, learning or decision-support criteria are applied.