Mean conservation for density estimation via diffusion using the finite element method
This work addresses the problem of preserving statistical moments in diffusion-based density estimation, but the contribution is incremental as it applies known boundary condition techniques to a specific numerical framework.
The paper proposes boundary conditions for the diffusion equation that preserve the mean and total mass of a data sample during density estimation, validated through 1D finite element experiments. The method is extended to 2D for future applications.
We propose boundary conditions for the diffusion equation that maintain the initial mean and the total mass of a discrete data sample in the density estimation process. A complete study of this framework with numerical experiments using the finite element method is presented for the one dimensional diffusion equation, some possible applications of this results are presented as well. We also comment on a similar methodology for the two-dimensional diffusion equation for future applications in two-dimensional domains.