Domain Adaptation with Interval-valued Observations: Theory and Algorithms

Unsupervised Domain Adaptation (UDA) focuses on enhancing the model performance on an unlabeled target domain by leveraging knowledge from a source domain. The source and target domains usually share different distributions. Existing UDA research primarily concentrates on image data characterized by crisp-valued features. However, interval-valued data, where all the observations’ features are described by intervals, is also a common type of data in real-world scenarios. For instance, measurement instruments are unable to provide exact numerical outcomes, instead employing intervals to describe their results. Hence, this paper focuses on the highly challenging context known as domain adaptation with interval-valued observations. In this environment, the objective is to improve classification accuracy within an unlabeled target domain by capitalizing on knowledge gleaned from a labeled source domain, where both domains exclusively feature interval-valued observations. To address this, we first establish an upper bound on the risk in the interval-valued target domain, underpinning our analysis with rigorous theoretical insights. Subsequently, guided by our theoretical analysis, a new model based on Takagi-Sugeno Fuzzy rules and a Self-supervised Pseudo-labeling strategy (SP-TSF) is developed to address the proposed problem. Takagi-Sugeno fuzzy rules are harnessed to handle the inherent uncertainty intrinsic to interval-valued data, while a pseudo-labeling strategy is developed to augment distribution alignment between the source and target domains, each characterized by interval-valued observations. Extensive experiments on both synthetic and realworld datasets verify the rationality of our theoretical analysis and the efficacy of the proposed model.