The effective embedding estimation of distribution and the construction of regression model with strong representation ability are two key problems of distribution regression. This paper proposes a random multi-scale kernel-based Bayesian distribution regression (RMK-BDR) learning framework. Vector-valued kernel mean embedding (KME) estimators with a same dimension which is chosen adaptively to the data are introduced in the first stage of distribution regression learning. Then, a linear combination of multi-scale Gaussian kernels with different scale parameters randomly sampled from a predefined distribution is used as the regression model. Sparsity priors are added on those linear combination weights. Under the Bayesian inference theory, a prediction distribution of the response variable is obtained. A series of experiment results verify the effectiveness of the proposed algorithm.

有效的分布嵌入估计和具有较强表示能力的回归模型的构建是分布回归的两个关键问题。本文提出了一种基于核的随机多尺度贝叶斯分布回归（RMK-BDR）学习框架。在分布回归学习的第一阶段中，引入了针对数据自适应选择的具有相同维的向量值核均值嵌入（KME）估计器。然后，将多尺度高斯核与从预定义分布中随机采样的不同尺度参数的线性组合用作回归模型。在这些线性组合权重上添加稀疏先验。在贝叶斯推理理论下，获得了响应变量的预测分布。