TAKDE: Temporal Adaptive Kernel Density Estimator for Real-Time Dynamic Density Estimation

TL;DR

TAKDE is a new theoretically grounded kernel density estimator designed for real-time dynamic density estimation, outperforming existing methods in accuracy and efficiency on synthetic and real-world data.

Contribution

The paper introduces TAKDE, a novel adaptive kernel density estimator with a theoretical AMISE bound, optimized for real-time dynamic density estimation.

Findings

TAKDE outperforms state-of-the-art estimators in test log-likelihood.

TAKDE achieves smaller runtime while maintaining high accuracy.

Theoretical analysis guides the design of TAKDE for optimal worst-case performance.

Abstract

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.