Continuous Target Shift Adaptation in Supervised Learning

Supervised learning in machine learning concerns inferring an underlying relation between covariate x and target y based on training covariate-target data. It is traditionally assumed that training data and test data, on which the generalization performance of a learning algorithm is measured, follow the same probability distribution. However, this standard assumption is often violated in many real-world applications such as computer vision, natural language processing, robot control, or survey design, due to intrinsic non-stationarity of the environment or inevitable sample selection bias. This situation is called dataset shift and has attracted a great deal of attention recently. In the paper, we consider supervised learning problems under the target shift scenario, where the target marginal distribution p(y) changes between the training and testing phases, while the target-conditioned covariate distribution p(x|y) remains unchanged. Although various methods for mitigating target shift in classification (a.k.a. class prior change) have been developed so far, few methods can be applied to continuous targets. In this paper, we propose methods for continuous target shift adaptation in regression and conditional density estimation. More specifically, our contribution is a novel importance weight estimator for continuous targets. Through experiments, the usefulness of the proposed method is demonstrated.