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 fully understood. To address numerical problems associated with normalizing logarithmic terms, we follow a geometric approximation based on the convex hull of input data. This ensures feasible, stable, and accurate inference in scenarios involving large amounts of data. Numerical experiments demonstrate substantially improved computational efficiency when handling large and complex datasets, thus laying the foundation for a broad range of applications within the statistics and machine learning communities.

翻译：高效可扩展的非参数或半参数回归分析与密度估计对统计学与机器学习领域至关重要。然而，现有方法在处理大规模数据时能力有限。我们通过为多变量条件变换模型（MCTMs）开发新型核心集构造方法来解决该问题，旨在增强其可扩展性与训练效率。据我们所知，这是首个针对半参数分布模型的核心集。该方法通过重要性采样实现显著的数据缩减，并以高概率确保对数似然保持在$(1\pm\varepsilon)$的乘法误差界内，从而维持统计模型的准确性。相较于此前已整合核心集的传统全参数模型，我们的半参数方法展现出更强的适应性，尤其适用于存在复杂分布与非线性关系但尚未完全理解的场景。为解决与对数项归一化相关的数值问题，我们采用了基于输入数据凸包的几何近似策略，确保在大规模数据场景中实现可行、稳定且准确的推断。数值实验表明，该方法在处理大规模复杂数据集时显著提升了计算效率，为统计学与机器学习领域的广泛应用奠定了基础。