论文标题
Takde：实时动态密度估计的时间自适应内核密度估计器
TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation
论文作者
论文摘要
实时密度估计在许多应用中无处不在，包括计算机视觉和信号处理。内核密度估计可以说是最常用的密度估计技术之一，使用“滑动窗口”机制可以使内核密度估计器适应动态过程。在本文中，我们得出了“滑动窗口”内核密度估计器的渐近平均综合平方误差（AMISE）上限。该上限提供了设计一种新型估计器的原则指南，我们将其命名为时间自适应核密度估计器（TAKDE）。与“滑动窗口”内核密度估计器的启发式方法相比，Takde在最差的案例中在理论上是最佳的。我们使用合成和现实世界数据集提供数值实验，这表明Takde的表现优于其他最先进的动态密度估计器（包括内核家族以外的动态密度估计器）。特别是，Takde以较小的运行时间实现了出色的测试日志样本。
Real-time density estimation is ubiquitous in many applications, including computer vision and signal processing. Kernel density estimation is arguably one of the most commonly used density estimation techniques, and the use of "sliding window" mechanism adapts kernel density estimators to dynamic processes. In this paper, we derive the asymptotic mean integrated squared error (AMISE) upper bound for the "sliding window" kernel density estimator. This upper bound provides a principled guide to devise a novel estimator, which we name the temporal adaptive kernel density estimator (TAKDE). Compared to heuristic approaches for "sliding window" kernel density estimator, TAKDE is theoretically optimal in terms of the worst-case AMISE. We provide numerical experiments using synthetic and real-world datasets, showing that TAKDE outperforms other state-of-the-art dynamic density estimators (including those outside of kernel family). In particular, TAKDE achieves a superior test log-likelihood with a smaller runtime.
