Active recursive Bayesian inference using Rényi information measures

Abstract

• An active recursive inference method based on Rényi information measures. • Posterior probability changes can enhance both query optimization and stopping criterion in the RBI process. • Using Rényi entropy and α -divergence unifies the multi-objective RBI problem. • The proposed unified framework enhances both speed and accuracy, in the presence of an adversarial prior. Recursive Bayesian inference (RBI) framework provides optimal Bayesian latent variable estimates in real-time settings with streaming noisy observations. Active RBI attempts to effectively select queries that lead to more informative observations to reduce uncertainty until the process is stopped at a certain confidence level. However, the mismatch between querying objective and stopping criterion creates the conundrum of improving the performance of one objective at the expense of deteriorating the other. Moreover, conventional active querying methods stagger in the presence of misleading prior information. Inspired by information theoretic approaches, we propose an active RBI framework where query and stopping criterion are jointly selected through a unified objective based on Rényi information measures. The proposed unified formulation enables us to jointly enhance speed and accuracy in the RBI process. We theoretically demonstrate that the proposed objective encourages exploration in the presence of misleading prior. Furthermore, we motivate our framework by proving a geometrical representation for active querying and decision making on a probability simplex. We provide empirical and experimental studies on two applications including restaurant recommendation and brain-computer interface (BCI) typing systems and demonstrate that our method outperforms comparable approaches by improving both speed and accuracy.