Federated Bounded-Memory Anytime-Valid Kernel Independence Testing for Structural Equation Models in Non-Stationary IoT Anomaly Detection

Federated Internet of Things deployments require anomaly detectors that respect strict memory limits while remaining statistically valid under non-stationary data streams. Conventional kernel independence tests, such as the Hilbert-Schmidt Independence Criterion, demand the retention of full Gram matrices, and their batch formulation cannot support sequential decision making; consequently, they are ill-suited to edge devices whose distributions drift over time. We propose a federated bounded-memory framework for anytime-valid kernel independence testing within structural equation models. Each node first embeds sensor variables and model residuals into a finite-dimensional Euclidean space through random Fourier features, and then maintains a decayed cross-covariance sketch whose memory footprint scales only with the square of the feature dimension. Anytime-valid e-values are constructed from a martingale wealth process driven by betting fractions, so that the false-alarm rate is controlled at a prescribed level irrespective of the stopping time. Furthermore, only quantized adjacency updates, compressed covariance sketches, and sample counts are transmitted to the server, where a weighted consensus update refines the global causal graph and shared structural parameters. The proposed method replaces the batch-based conditional independence tester in the causal inference engine, and its continuous e-value output feeds the anomaly scoring module and the federated graph coordinator, thereby closing the loop between causal discovery and equation fitting. Experiments on non-stationary IoT benchmarks assess detection accuracy, communication cost and memory consumption. The framework attains constant memory usage and linear per-step time complexity, and it therefore offers a practical route to rigorous, privacy-preserving causal anomaly detection at the network edge.