Abstract
We consider the sequential change point detection problem in linear causal graphs that explicitly incorporates interventions. In such graphs, changes can propagate through the graph structure to multiple nodes. Under a single-change setting, we introduce a centralization technique that characterizes how the change propagated across nodes can be concentrated into a single dimension. For an edge change, we further show that appropriately selecting the intervention node can amplify the magnitude of the change, thereby improving detection performance. Accordingly, we develop an algorithm for setting intervention values, which facilitates the identification of optimal intervention nodes based on Kullback-Leibler divergence. Using these intervention values, we further propose two change detection methods, each equipped with an adaptive intervention policy that balances exploration and exploitation. Under a single-change setting, we establish the first-order asymptotic optimality of the proposed methods, and further evaluate their empirical performance, including robustness under multiple changes, through simulations and two case studies.