Dynamic density estimation is ubiquitous in many applications, including computer vision and signal processing. One popular method to tackle this problem is the "sliding window" kernel density estimator. There exist various implementations of this method that use heuristically defined weight sequences for the observed data. The weight sequence, however, is a key aspect of the estimator affecting the tracking performance significantly. In this work, we study the exact mean integrated squared error (MISE) of "sliding window" Gaussian Kernel Density Estimators for evolving Gaussian densities. We provide a principled guide for choosing the optimal weight sequence by theoretically characterizing the exact MISE, which can be formulated as constrained quadratic programming. We present empirical evidence with synthetic datasets to show that our weighting scheme indeed improves the tracking performance compared to heuristic approaches.

翻译：动态密度估计在计算机视觉和信号处理等众多应用中普遍存在。解决该问题的一种常用方法是“滑动窗口”核密度估计器。该方法有多种实现方式，它们对观测数据使用基于启发式定义的权重序列。然而，权重序列是影响跟踪性能的关键因素。在本研究中，我们精确分析了针对演化高斯密度的“滑动窗口”高斯核密度估计器的均方积分误差（MISE）。通过理论刻画精确MISE（可表述为约束二次规划问题），我们为选择最优权重序列提供了原则性指导。我们使用合成数据集进行的实证研究表明，与启发式方法相比，所提出的加权方案确实提升了跟踪性能。