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

arXiv: https://arxiv.org/abs/2203.08317 · HTML: https://mlsanity.com/paper/2203.08317/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 36 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 3 of 3)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Kernel Density Estimation for Dynamical Systems](https://mlsanity.com/paper/1607.03792/) (2016)
- [Dynamic density estimation with diffusive Dirichlet mixtures](https://mlsanity.com/paper/1410.2477/) (2014)

## Built on by (most cited first, 4 of 4)

- [TAP: The Attention Patch for Cross-Modal Knowledge Transfer from Unlabeled Modality](https://mlsanity.com/paper/2302.02224/) (2023)
- [Tracking Dynamic Gaussian Density with a Theoretically Optimal Sliding Window Approach](https://mlsanity.com/paper/2403.07207/) (2024)
- [Sublinear Sketches for Approximate Nearest Neighbor and Kernel Density Estimation](https://mlsanity.com/paper/2510.23039/) (2025)
- [Predictive Hotspot Mapping for Data-driven Crime Prediction](https://mlsanity.com/paper/2602.23750/) (2026)

## Abstract (arXiv)

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.