A method is provided for root cause anomaly detection in an invariant network having a plurality of nodes that generate time series data. The method includes modeling anomaly propagation in the network. The method includes reconstructing broken invariant links in an invariant graph based on causal anomaly ranking vectors. Each broken invariant link involves a respective node pair formed from the plurality of nodes such that one of the nodes in the respective node pair has an anomaly. Each causal anomaly ranking vector is for indicating a respective node anomaly status for a given one of the plurality of nodes when paired. The method includes calculating a sparse penalty of the casual anomaly ranking vectors to obtain a set of time-dependent anomaly rankings. The method includes performing temporal smoothing of the set of rankings, and controlling an anomaly-initiating one of the plurality of nodes based on the set of rankings.