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 $\alpha$-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.

中文翻译：

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使用 $\alpha$-Divergence 进行后轨迹分析的主动递归贝叶斯推理

递归贝叶斯推理 (RBI) 在实时设置中提供最佳贝叶斯潜在变量估计，并具有流式噪声观测。主动 RBI 尝试有效地选择导致更多信息观察的查询，以快速减少不确定性，直到做出自信的决定。然而，推理和查询机制的最优性目标通常不是联合选择的。此外，传统的主动查询方法由于误导性先验信息而错开。受信息论方法的启发，我们提出了一个主动 RBI 框架，通过 Renyi 熵和 $\alpha$-divergence 统一推理和查询选择步骤。我们还提出了一个基于 Renyi 熵及其变化的新目标，称为 Momentum，鼓励对误导性先前案例的探索。提出的主动 RBI 框架应用于概率单纯形中后验变化的轨迹，提供具有指定置信度的协调主动查询和决策。在某些假设下，我们通过分析证明所提出的方法通过允许选择不太可能的事件来优于传统方法，例如互信息。我们对两个应用程序进行了实证和实验性能评估：餐厅推荐和脑机接口 (BCI) 打字系统。我们通过分析证明，通过允许选择不太可能的事件，所提出的方法优于传统方法，例如互信息。我们对两个应用程序进行了实证和实验性能评估：餐厅推荐和脑机接口 (BCI) 打字系统。我们通过分析证明，通过允许选择不太可能的事件，所提出的方法优于传统方法，例如互信息。我们对两个应用程序进行了实证和实验性能评估：餐厅推荐和脑机接口 (BCI) 打字系统。