We study an agent who chooses a profile of actions between which she may misperceive the correlation. Our agent cannot be modeled by reducing every action profile to an act, as implied by the usual monotonicity axiom. We introduce a novel framework that explicitly considers action profiles and axiomatically characterize a model that relaxes monotonicity but retains the rest of the expected utility axioms. Our agent acts as if she attaches a probability to each possible correlation structure and then maximizes expected utility using her (possibly misspecified) beliefs. This representation nests several models used in the behavioral game theory literature to consider imperfect inference, including correlation neglect.