Random multi-scale kernel-based Bayesian distribution regression learning

摘要

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.