human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "submodular functions from discrete to continous domains"):
  Abstract: Submodular set-functions have many applications in combinatorial optimization, as they can be minimized and approximately maximized in polynomial time. A key element in many of the algorithms and analyses is the possibility of extending the submodular set-function to a convex function, which opens up tools from convex optimization. Submodularity goes beyond set-functions and has naturally been considered for problems with multiple labels or for functions defined on continuous domains, where it corresponds essentially to cross second-derivatives being nonpositive. In this paper, we show that most results relating submodularity and convexity for set-functions can be extended to all submodular functions. In particular, (a) we naturally define a continuous extension in a set of probability measures, (b) show that the extension is convex if and only if the original function is submodular, (c) prove that the problem of minimizing a submodular function is equivalent to a typically non-smooth convex optimization problem, and (d) propose another convex optimization problem with better computational properties (e.g., a smooth dual problem). Most of these extensions from the set-function situation are obtained by drawing links with the theory of multi-marginal optimal transport, which provides also a new interpretation of existing results for set-functions. We then provide practical algorithms to minimize generic submodular functions on discrete domains, with associated convergence rates.

Includes members:
  Member "scalable variational inference in log supermodular models":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "flexible modeling of diversity with strongly log concave distributions")
  Member "reflection methods for user friendly submodular optimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "quadratic decomposable submodular function minimization theory and practice")
  Member "duality between subgradient and conditional gradient methods":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "safe screening for the generalized conditional gradient method")
  Member "learning with submodular functions a convex optimization perspective":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "online non monotone dr submodular maximization")
  Member "minimizing a sum of submodular functions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "localized flow based clustering in hypergraphs")
  Member "iterative hard thresholding for compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efficient active learning of sparse halfspaces with arbitrary bounded noise")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.LG(Machine Learning)