Posterior Adaptation With New Priors

TL;DR

This paper introduces a method to adapt posterior probabilities to changing class priors by recovering data likelihoods from original posteriors and priors, enabling dynamic updates without retraining.

Contribution

It provides a unique solution to recover data likelihoods from posteriors and priors, facilitating posterior adaptation with new priors in a simple, computationally efficient manner.

Findings

Allows dynamic posterior updates with new priors

Provides a unique likelihood recovery solution

Enables adaptation without retraining

Abstract

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.