Sensitivity-Aware Density Estimation in Multiple Dimensions
Machine Learning
2025-06-04 v1 Artificial Intelligence
Computational Engineering, Finance, and Science
Data Structures and Algorithms
Signal Processing
Abstract
We formulate an optimization problem to estimate probability densities in the context of multidimensional problems that are sampled with uneven probability. It considers detector sensitivity as an heterogeneous density and takes advantage of the computational speed and flexible boundary conditions offered by splines on a grid. We choose to regularize the Hessian of the spline via the nuclear norm to promote sparsity. As a result, the method is spatially adaptive and stable against the choice of the regularization parameter, which plays the role of the bandwidth. We test our computational pipeline on standard densities and provide software. We also present a new approach to PET rebinning as an application of our framework.
Cite
@article{arxiv.2506.02323,
title = {Sensitivity-Aware Density Estimation in Multiple Dimensions},
author = {Aleix Boquet-Pujadas and Pol del Aguila Pla and Michael Unser},
journal= {arXiv preprint arXiv:2506.02323},
year = {2025}
}