The Effect of the Prior on Asymptotic Performance of Uncertain Naïve Bayesian Networks
Lance Kaplan, James Z. Hare, Parth Paritosh · 2025
In this work, we analyze limited knowledge about likelihoods in traditional fusion as an uncertain Naïve Bayesian network whose conditional probabilities are known within posterior Dirichlet distributions reflected of limited training data. In prior work, we showed that inferences from these uncertain networks are confidently precise despite finite training data as the number of features goes to infinity for a uniform prior. The inference is usually correct except for pathological cases that diminish as the training data size goes to infinity. This work extends the analysis by studying how various priors affect asymptotic inference when the priors do or do not match the generative process for the conditional probabilities. Furthermore, the work analyzes how the prior affects the convergence rate of the inference.