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 "maximizing submodular functions using probabilistic graphical models"):
  Abstract: We consider the problem of maximizing submodular functions; while this problem is known to be NP-hard, several numerically efficient local search techniques with approximation guarantees are available. In this paper, we propose a novel convex relaxation which is based on the relationship between submodular functions, entropies and probabilistic graphical models. In a graphical model, the entropy of the joint distribution decomposes as a sum of marginal entropies of subsets of variables; moreover, for any distribution, the entropy of the closest distribution factorizing in the graphical model provides an bound on the entropy. For directed graphical models, this last property turns out to be a direct consequence of the submodularity of the entropy function, and allows the generalization of graphical-model-based upper bounds to any submodular functions. These upper bounds may then be jointly maximized with respect to a set, while minimized with respect to the graph, leading to a convex variational inference scheme for maximizing submodular functions, based on outer approximations of the marginal polytope and maximum likelihood bounded treewidth structures. By considering graphs of increasing treewidths, we may then explore the trade-off between computational complexity and tightness of the relaxation. We also present extensions to constrained problems and maximizing the difference of submodular functions, which include all possible set functions.

Includes members:
  Member "maximum likelihood bounded tree width markov networks":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient learning of optimal markov network topology with k tree modeling")
  Member "fast semidifferential based submodular function optimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "robust submodular minimization with applications to cooperative modeling")
  Member "convex relaxations for learning bounded treewidth decomposable graphs":
    also connected through other hyperedges:
      (none)
  Member "a submodular supermodular procedure with applications to discriminative structure learning":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a unified framework of robust submodular optimization")
  Member "a new class of upper bounds on the log partition function":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "visual semantic information pursuit a survey")
  Member "pac learning bounded tree width graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "efficient learning of optimal markov network topology with k tree modeling")
  Member "near optimal nonmyopic value of information in graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the unreasonable effectiveness of the greedy algorithm greedy adapts to sharpness")
  Member "learning with submodular functions a convex optimization perspective":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "online non monotone dr submodular maximization")

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)