DistributionMatchingforCrowdCounting SupplementaryMaterial

Finally in Section 4 we show the leaderboard ranking record on the time of the main paper submission. Before proving the proposed theorems in the main paper, we state the following two theorems, introducedin[7,9]. Then, `(x,x0) is 1-Lipschitz w.r.t. If α min < β min, without loss of generality, letα k = α min. The newsolution(α,β)does not violate the constraints in Eq. (16) and increases the objective.