Kernel Conditional Density Operators

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Ingmar Schuster, Mattes Mollenhauer, Stefan Klus, Krikamol Muandet ;
Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics, PMLR 108:993-1004, 2020.

Abstract

We introduce a novel conditional density estimationmodel termed the conditional densityoperator (CDO). It naturally captures multivariate,multimodal output densities andshows performance that is competitive withrecent neural conditional density models andGaussian processes. The proposed model isbased on a novel approach to the reconstructionof probability densities from their kernelmean embeddings by drawing connections toestimation of Radon-Nikodym derivatives inthe reproducing kernel Hilbert space (RKHS).We prove finite sample bounds for the estimationerror in a standard density reconstructionscenario, independent of problem dimensionality.Interestingly, when a kernel is used thatis also a probability density, the CDO allowsus to both evaluate and sample the outputdensity efficiently. We demonstrate the versatilityand performance of the proposed modelon both synthetic and real-world data.

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