对贝叶斯滤波进行温控以提升基于模型的估计
Tempering the Bayes Filter towards Improved Model-Based Estimation
AI总结：
本文提出温控贝叶斯滤波器，通过温控似然和后验提升预测精度，适用于线性高斯情况得到温控卡尔曼滤波器。
摘要：
基于模型的滤波通常是在不完美模型的约束下进行的，因为学习部分可观测的随机系统仍然是一项挑战。最近关于贝叶斯推断的研究发现，对不完美模型的似然或完整后验进行温控可以提高预测准确性，以期望负对数似然来衡量。在本文中，我们开发了温控贝叶斯滤波器，通过上述两种方法以及一种新引入的模式来提高估计性能。结果允许递归实现，计算复杂度不超过原始贝叶斯滤波器。我们的分析揭示了——除了贝叶斯推断领域众所周知的事实，即似然温控影响先验和似然之间的平衡之外，完整后验温控调节最终信念分布的熵水平。我们进一步发现，温控空间中的一个区域可以被理解为在贝叶斯滤波器和MAP滤波器之间进行插值，恢复这些作为特殊情况。分析结果进一步建立了温控贝叶斯滤波器在何种条件下能够实现改进的预测性能的条件。将结果专门应用于线性高斯情况，我们得到温控卡尔曼滤波器。在此背景下，我们解释了参数如何影响卡尔曼状态估计和协方差传播。实证结果证实了我们的方法在贝叶斯滤波器基准上的一致性改进。
英文摘要：
Model-based filtering is often carried out while subject to an imperfect model, as learning partially-observable stochastic systems remains a challenge. Recent work on Bayesian inference found that tempering the likelihood or full posterior of an imperfect model can improve predictive accuracy, as measured by expected negative log likelihood. In this paper, we develop the tempered Bayes filter, improving estimation performance through both of the aforementioned, and one newly introduced, modalities. The result admits a recursive implementation with a computational complexity no higher than that of the original Bayes filter. Our analysis reveals that -- besides the well-known fact in the field of Bayesian inference that likelihood tempering affects the balance between prior and likelihood -- full-posterior tempering tunes the level of entropy in the final belief distribution. We further find that a region of the tempering space can be understood as interpolating between the Bayes- and MAP filters, recovering these as special cases. Analytical results further establish conditions under which a tempered Bayes filter achieves improved predictive performance. Specializing the results to the linear Gaussian case, we obtain the tempered Kalman filter. In this context, we interpret how the parameters affect the Kalman state estimate and covariance propagation. Empirical results confirm that our method consistently improves predictive accuracy over the Bayes filter baseline.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
