Sensitivity-Aware Density Estimation in Multiple Dimensions
By: Aleix Boquet-Pujadas, Pol del Aguila Pla, Michael Unser
Potential Business Impact:
Makes computers better at guessing patterns in messy data.
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.
Similar Papers
Nonparametric spectral density estimation from irregularly sampled data
Methodology
Find patterns in messy, scattered data.
Bayesian Multivariate Density-Density Regression
Methodology
Finds hidden patterns in complex data.
Nonparametric spectral density estimation using interactive mechanisms under local differential privacy
Statistics Theory
Keeps data private while learning patterns.