自适应带宽核密度估计

Question

似乎有大量的信息和工具可用于实现标准的多元或单变量核密度估计。然而，我目前使用的离散地理数据特别稀疏，并且倾向于聚集在人口密度较高的地区。在

也就是说，我在地图上有很多点（经度和纬度），我想估算一个给定点的概率密度，但我需要某种方式对人口密度进行规范化。环顾四周，这类问题的正确方法似乎应该是为核估计实现某种最近邻自适应带宽。然而，似乎高斯统计不支持自适应带宽。有没有人知道我是如何实现这一点的，或者是否有适用于自适应带宽KDE的软件包？在

Answer 1

我在Python中搜索可变/自适应内核密度估计包时遇到了这个问题。我知道手术可能已经很久了，但我还是发现了：

• AdaptiveKDE（自适应核密度估计的Python模块）

  This package implements adaptive kernel density estimation algorithms for 1-dimensional signals developed by Hideaki Shimazaki. This enables the generation of smoothed histograms that preserve important density features at multiple scales, as opposed to naive single-bandwidth kernel density methods that can either over or under smooth density estimates.

• awkde（高斯核自适应宽度KDE）

  The kernel bandwith is choosen locally to account for variations in the density of the data. Areas with large density gets smaller kernels and vice versa. This smoothes the tails and gets high resolution in high statistics regions.

  This uses the awesome pybind11 package which makes creating C++ bindings super convenient. Only the evaluation is written in a small C++ snippet to speed it up, the rest is a pure python implementation.

{a3}是一个自适应分布，但它不适合于一个多模态分布。在

• KDEpy（Python中的内核密度估计）

  This Python 3.5+ package implements various kernel density estimators (KDE). Three algorithms are implemented through the same API: NaiveKDE, TreeKDE and FFTKDE. The class FFTKDE outperforms other popular implementations, see the comparison page.