Federated Naive Bayes with Real Mixture of Gaussians and Institutional Governance Regularization for Network Intrusion Detection
About
Federated learning for intrusion detection rests on a flawed premise: that every participating institution contributes equally to the shared model. In practice, a financial institution with mature security controls and low vulnerability exposure produces fundamentally different data than a government agency running with weaker controls and higher exposure. Treating their local models as equivalent discards information that organisations already collect through standard risk management audits. Four governance indicators from the CRISC framework of ISACA, specifically control maturity (CMM), proportion of implemented controls (KCI), risk indicator activation frequency (KRI), and mean vulnerability score (CVSS), are combined here into an Institutional Coherence Index (ICC). This index enters a Nelder-Mead federated weight optimizer as a regularization prior, guiding weight assignment toward institutional quality without imposing any fixed allocation. Each node trains a hybrid local classifier combining Categorical and Gaussian Naive Bayes. The server combines local distributions as a real Mixture of Gaussians, preserving each node's statistical identity rather than collapsing it into a global parameter vector. Validation on NSL-KDD (2009), CIC-IDS2017 (2017), and UNSW-NB15 (2015), under seven Dirichlet heterogeneity levels, shows that the ICC-regularized proposal outperforms size-proportional federated averaging in all three datasets: F1-macro 0.9135 vs. 0.9076 (+0.0059), 0.7556 vs. 0.6771 (+0.0785), and 0.2110 vs. 0.2060 (+0.0050). Statistical significance holds in 70 of 94 configurations (McNemar, p < 0.05). In all three cases, the optimizer assigned the highest weight to the institutionally most mature node and the lowest to the least mature, without any explicit ordering constraint.