A Proof of Lemma 4.4 The first stage of Algorithm 1 outputs an entity level

A.1 The Feldman-Langberg framework We first give the definition of query space and the corresponding coresets. Specifically, if u(x) = 1 for all x X, we use ( X, P,f) for simplicity. Due to the separability of f, we have the following coreset definition. Then by Definition A.2, Lemma 4.4 represents that Now we are ready to give the Feldman-Langberg framework. We also introduce a notion which measures the combinatorial complexity of a query space.