提出一种自适应密度估计方法，可处理不均匀采样下的多维概率密度建模。
Sensitivity-Aware Density Estimation in Multiple Dimensions
- 用样条网格结合核范数正则化优化密度估计，提升空间适应性。
- 在标准密度测试中表现稳定，对正则化参数不敏感，相当于带宽自适应。
- 适用于高维探测器灵敏度建模，如正电子发射断层扫描重嵌套应用。
我们提出一个优化问题，用于在非均匀采样条件下进行多维概率密度估计。该方法将探测器灵敏度视为异质密度，并利用样条插值在网格上的计算高效性与灵活边界条件。通过核范数正则化样条的海森矩阵，促进稀疏性，使方法具备空间自适应性和对正则化参数（相当于带宽）选择的鲁棒性。我们在标准密度上验证了该计算流程，并提供了开源软件。此外，还将该框架应用于正电子发射断层扫描（PET）重嵌套，提出新方法。
原文摘要 · Abstract (English)
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.
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