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Given an n × d dimensional dataset A, a projection query specifies a subset C ⊆ [d] of columns which yields a new n × |C| array. We study the space complexity of computing data analysis functions over such subspaces, including heavy hitters and norms, when the subspaces are revealed only after observing the data. We show that this important class of problems is typically hard: for many problems, we show 2^Ω(d) lower bounds. However, we present upper bounds which demonstrate space dependencyarXiv:2101.07546v1 fatcat:z7eyi6jm5jhoxenwuotooqy47i