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The reliability of inferences made by data-driven systems hinges on the data's continued conformance to the systems' initial settings and assumptions. When serving data (on which we want to apply inference) deviates from the profile of the initial training data, the outcome of inference becomes unreliable. We introduce conformance constraints, a new data profiling primitive tailored towards quantifying the degree of non-conformance, which can effectively characterize if inference over that tuple is untrustworthy. Conformance constraints are constraints over certain arithmetic expressions (called projections) involving the numerical attributes of a dataset, which existing data profiling primitives such as functional dependencies and denial constraints cannot model. Our key finding is that projections that incur low variance on a dataset construct effective conformance constraints. This principle yields the surprising result …