  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.
