We develop a new framework for estimating joint probability distributions using tensor product reproducing kernel Hilbert spaces (RKHS). Our framework accommodates a low-dimensional, normalized and positive model of a Radon--Nikodym derivative, which we estimate from sample sizes of up to several millions, alleviating the inherent limitations of RKHS modeling. Well-defined normalized and positive conditional distributions are natural by-products to our approach. Our proposal is fast to compute and accommodates learning problems ranging from prediction to classification. Our theoretical findings are supplemented by favorable numerical results.

翻译：我们提出了一种基于张量积再生核希尔伯特空间（RKHS）的联合概率分布估计新框架。该框架采用低维、归一化且正的Radon-Nikodym导数模型，通过处理高达数百万的样本量来缓解RKHS建模的固有局限性。定义明确的归一化正条件分布是本方法的自然副产品。该方案计算速度快，适用于从预测到分类的各类学习问题。理论研究成果得到了优良数值实验结果的佐证。