Along line ofwork has established convergence rates ofthe empirical distribution tothe true distribution in spaces as general as unbounded metric spaces [54, 25, 45]). In the Euclidean setting, this is well understood [14,2,18], although, to the best of our knowledge, minimax lower bounds have been proven only recently [45]; this setting intersects with our work in the caseσd = 1,σg = 0, pd =,matchingourminimaxrateofn 1/D+n 1/2.

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(Theorem 4). We also consider Assumption 3. Note that this assumption does not restrict the class of considered Iterative algorithms are traditionally evaluated based on their gradient complexity .

Then, one can adopt theprinciple of separatingthe presence of an entity and its instantiation parameters into capsule length and orientation, respectively. In particular, we use the lengths of capsules to score the presence of entity classes corresponding to different subspaces, while their orientations are used to instantiate the parameters of entity properties such as poses, scales, deformations and textures.

We propose a generalized variant of Frank-Wolfe algorithm for solving a class ofsparse/low-rank optimization problems.

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