Maximum Mean Discrepancy (MMD)

Maximum Mean Discrepancy is a kernel-based two-sample test that asks whether two batches of data come from the same underlying distribution. Each batch is mapped into a reproducing kernel Hilbert space and the test statistic is the squared distance between their mean embeddings. Under a characteristic kernel (RBF with bandwidth set by the median heuristic, in Concord's case), the statistic is zero only when the two distributions are identical. A permutation test produces an empirical p-value without parametric assumptions. Concord by IaxaI's drift detector uses MMD on rolling windows of input events, output OCSF events, and entity baselines. The reference window is the known-good recent past (e.g., the previous 24 hours). The test window is the current short window (e.g., the previous hour). When MMD fires above its severity threshold, the auto-repair loop activates. MMD is cheap, deterministic, and parameter-light, which is exactly what the hot path needs.