Repository: Freie Universit├Ąt Berlin, Math Department

Kernel Conditional Density Operators

Schuster, Ingmar and Mollenhauer, Mattes and Klus, Stefan and Muandet, K. (2020) Kernel Conditional Density Operators. In: 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), August 26 - 28, 2020, Online.

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We introduce a novel conditional density estimation model termed the conditional density operator (CDO). It naturally captures multivariate, multimodal output densities and shows performance that is competitive with recent neural conditional density models and Gaussian processes. The proposed model is based on a novel approach to the reconstruction of probability densities from their kernel mean embeddings by drawing connections to estimation of Radon-Nikodym derivatives in the reproducing kernel Hilbert space (RKHS). We prove finite sample bounds for the estimation error in a standard density reconstruction scenario, independent of problem dimensionality. Interestingly, when a kernel is used that is also a probability density, the CDO allows us to both evaluate and sample the output density efficiently. We demonstrate the versatility and performance of the proposed model on both synthetic and real-world data.

Item Type:Conference or Workshop Item (Paper)
Additional Information:Proceedings of AISTATS 2020
Subjects:Mathematical and Computer Sciences > Mathematics > Applied Mathematics
Divisions:Department of Mathematics and Computer Science > Institute of Mathematics > Deterministic and Stochastic PDEs Group
ID Code:3099
Deposited By: Ulrike Eickers
Deposited On:19 Feb 2024 14:29
Last Modified:19 Feb 2024 14:29

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