# Sensitivity-Aware Density Estimation in Multiple Dimensions

arXiv: https://arxiv.org/abs/2506.02323 · HTML: https://mlsanity.com/paper/2506.02323/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 3 of its 63 references that are in the map.
- First posted on arXiv 2 Jun 2025.

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

- [Probit transformation for kernel density estimation on the unit interval](https://mlsanity.com/paper/1303.4121/) (2013)
- [Improving "Fast Iterative Shrinkage-Thresholding Algorithm": Faster, Smarter and Greedier](https://mlsanity.com/paper/1811.01430/) (2018)
- [Convex Quantization Preserves Logconcavity](https://mlsanity.com/paper/2206.05598/) (2022)

## Abstract (arXiv)

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.