Adaptive machine learning (ML) aims to allow ML models to adapt to ever-changing environments with potential concept drift after model deployment. Traditionally, adaptive ML requires a new dataset to be manually labeled to tailor deployed models to altered data distributions. Recently, an interactive causality based self-labeling method was proposed to autonomously associate causally related data streams for domain adaptation, showing promising results compared to traditional feature similarity-based semi-supervised learning. Several unanswered research questions remain, including self-labeling's compatibility with multivariate causality and the quantitative analysis of the auxiliary models used in the self-labeling. The auxiliary models, the interaction time model (ITM) and the effect state detector (ESD), are vital to the success of self-labeling. This paper further develops the self-labeling framework and its theoretical foundations to address these research questions. A framework for the application of self-labeling to multivariate causal graphs is proposed using four basic causal relationships, and the impact of non-ideal ITM and ESD performance is analyzed. A simulated experiment is conducted based on a multivariate causal graph, validating the proposed theory.
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