TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation
This work addresses real-time density estimation for applications like computer vision and signal processing, offering a theoretically optimal solution that is incremental over heuristic approaches.
The paper tackles the problem of real-time dynamic density estimation by deriving an asymptotic mean integrated squared error (AMISE) upper bound for sliding window kernel density estimators, leading to the development of TAKDE, which outperforms state-of-the-art methods with superior test log-likelihood and smaller runtime.
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.