2019/05/27 by Ingmar Schuster, Schuster, Ingmar, Mattes Mollenhauer +5 · 2 citations
Computer Science · #FOS: Computer and information sciences #FOS: Mathematics #Gaussian Processes and Bayesian Inference #Machine Learning (cs.LG) #Machine Learning (stat.ML) #Neural Networks and Applications #Statistics Theory (math.ST) #Target Tracking and Data Fusion in Sensor Networks
paper · pdf · doi:10.48550/arxiv.1905.11255
openalex publication_date 2019/05/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.