Semi-parametric Spatial Intensity Estimation with Bandwidth Selection on KDE-NN based model

Music City Center 

In spatial point processes intensity estimation, traditional methods like kernel estimators and regression models have been effective in estimating the intensity function of a spatial point pattern. However, they fall short when dealing with nonlinear correlations. Deep learning models, such as Neural Networks(NN), and Variational AutoEncoders (VAE), offer a promising alternative to address these limitations due to their inherent properties and settings. These are widely used and acknowledged for their flexibility and capability to handle complex, nonlinear relationships. In this study, we additionally incorporate a bandwidth trainable KDE layer to our model, the KDE-NN based model provides additional flexibility to capture any spatial correlation in the data, while also controlling the degree of smoothness.

Spatial Intensity Estimation

Deep Learning Model

Bandwidth Selection

Kernel Density Estimation 

Section on Nonparametric Statistics