[2603.19792] Scalable Learning of Multivariate Distributions via Coresets

Computer Science > Machine Learning arXiv:2603.19792 (cs) [Submitted on 20 Mar 2026] Title:Scalable Learning of Multivariate Distributions via Coresets Authors:Zeyu Ding, Katja Ickstadt, Nadja Klein, Alexander Munteanu, Simon Omlor View a PDF of the paper titled Scalable Learning of Multivariate Distributions via Coresets, by Zeyu Ding and Katja Ickstadt and Nadja Klein and Alexander Munteanu and Simon Omlor View PDF HTML (experimental) Abstract:Efficient and scalable non-parametric or semi-parametric regression analysis and density estimation are of crucial importance to the fields of statistics and machine learning. However, available methods are limited in their ability to handle large-scale data. We address this issue by developing a novel coreset construction for multivariate conditional transformation models (MCTMs) to enhance their scalability and training efficiency. To the best of our knowledge, these are the first coresets for semi-parametric distributional models. Our approach yields substantial data reduction via importance sampling. It ensures with high probability that the log-likelihood remains within multiplicative error bounds of $(1\pm\varepsilon)$ and thereby maintains statistical model accuracy. Compared to conventional full-parametric models, where coresets have been incorporated before, our semi-parametric approach exhibits enhanced adaptability, particularly in scenarios where complex distributions and non-linear relationships are present, but not fu...