Active recursive Bayesian inference using Rényi information measures
This work addresses active inference problems in real-time systems like recommendation engines and brain-computer interfaces, offering an incremental improvement over existing methods.
The paper tackles the problem of active recursive Bayesian inference where conventional methods struggle with misleading prior information and lack joint optimization of inference and query selection. The authors propose a framework using Rényi information measures with a Momentum objective that encourages exploration, demonstrating analytical and empirical improvements over conventional methods like mutual information in restaurant recommendation and BCI typing applications.
Recursive Bayesian inference (RBI) 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 rapidly reduce uncertainty until a confident decision is made. However, typically the optimality objectives of inference and query mechanisms are not jointly selected. Furthermore, conventional active querying methods stagger due to misleading prior information. Motivated by information theoretic approaches, we propose an active RBI framework with unified inference and query selection steps through Renyi entropy and $α$-divergence. We also propose a new objective based on Renyi entropy and its changes called Momentum that encourages exploration for misleading prior cases. The proposed active RBI framework is applied to the trajectory of the posterior changes in the probability simplex that provides a coordinated active querying and decision making with specified confidence. Under certain assumptions, we analytically demonstrate that the proposed approach outperforms conventional methods such as mutual information by allowing the selections of unlikely events. We present empirical and experimental performance evaluations on two applications: restaurant recommendation and brain-computer interface (BCI) typing systems.