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In submodular optimization we often deal with the expected value of a submodular function f on a distribution 𝒟 over sets of elements. In this work we study such submodular expectations for negatively dependent distributions. We introduce a natural notion of negative dependence, which we call Weak Negative Regression (WNR), that generalizes both Negative Association and Negative Regression. We observe that WNR distributions satisfy Submodular Dominance, whereby the expected value of f under 𝒟arXiv:2207.04957v1 fatcat:mflbhtxelval5fmkhnvi6pl6ce