We develop a new framework for embedding joint probability distributions in 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 million data points, alleviating the inherent limitations of RKHS modeling. Well-defined normalized and positive conditional distributions are natural by-products to our approach. The embedding is fast to compute and accommodates learning problems ranging from prediction to classification. Our theoretical findings are supplemented by favorable numerical results.

翻译：我们提出了一种新的框架，用于在张量积再生核希尔伯特空间（RKHS）中嵌入联合概率分布。该框架支持拉德-尼科迪姆导数的低维、归一化且正定的模型，我们能够从多达数百万个数据点的样本量中对其进行估计，从而缓解了RKHS建模固有的局限性。明确定义的归一化且正定的条件分布是我们方法的自然副产品。该嵌入计算快速，并适用于从预测到分类的各种学习问题。我们的理论发现得到了有利数值结果的补充。