The specification describes data processes for analyzing large data steams for target anomalies. “Sequential dependencies” (SDs) are chosen for ordered data and present a framework for discovering which subsets of the data obey a given sequential dependency. Given an interval G, an SD on attributes X and Y, written as X→G Y, denotes that the distance between the Y-values of any two consecutive records, when sorted on X, are within G. SDs may be extended to Conditional Sequential Dependencies (CSDs), consisting of an underlying SD plus a representation of the subsets of the data that satisfy the SD. The conditional approximate sequential dependencies may be expressed as pattern tableaux, i.e., compact representations of the subsets of the data that satisfy the underlying dependency.