Sensitivity-Aware Density Estimation in Multiple Dimensions
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912410917404672 |
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| author | Boquet-Pujadas, Aleix Pla, Pol del Aguila Unser, Michael |
| author_facet | Boquet-Pujadas, Aleix Pla, Pol del Aguila Unser, Michael |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_02323 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Sensitivity-Aware Density Estimation in Multiple Dimensions Boquet-Pujadas, Aleix Pla, Pol del Aguila Unser, Michael Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science Data Structures and Algorithms Signal Processing 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. |
| title | Sensitivity-Aware Density Estimation in Multiple Dimensions |
| topic | Machine Learning Artificial Intelligence Computational Engineering, Finance, and Science Data Structures and Algorithms Signal Processing |
| url | https://arxiv.org/abs/2506.02323 |