Posterior Adaptation With New Priors
This solves a problem for classification systems where prior probabilities shift, though it appears incremental as it builds on existing Bayesian methods.
The paper addresses the degradation of classification performance when class priors change by proving a method to recover data likelihoods from original posteriors and priors, enabling recomputation of posteriors with new priors using Bayes' Rule, which is simple and allows dynamic updates.
Classification approaches based on the direct estimation and analysis of posterior probabilities will degrade if the original class priors begin to change. We prove that a unique (up to scale) solution is possible to recover the data likelihoods for a test example from its original class posteriors and dataset priors. Given the recovered likelihoods and a set of new priors, the posteriors can be re-computed using Bayes' Rule to reflect the influence of the new priors. The method is simple to compute and allows a dynamic update of the original posteriors.