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 "getting feasible variable estimates from infeasible ones mrf local polytope study"):
  Abstract: This paper proposes a method for construction of approximate feasible primal solutions from dual ones for large-scale optimization problems possessing certain separability properties. Whereas infeasible primal estimates can typically be produced from (sub-)gradients of the dual function, it is often not easy to project them to the primal feasible set, since the projection itself has a complexity comparable to the complexity of the initial problem. We propose an alternative efficient method to obtain feasibility and show that its properties influencing the convergence to the optimum are similar to the properties of the Euclidean projection. We apply our method to the local polytope relaxation of inference problems for Markov Random Fields and demonstrate its superiority over existing methods.

Includes members:
  Member "bethe admm for tree decomposition based parallel map inference":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "map inference via l2 sphere linear program reformulation")
  Member "efficient mrf energy minimization via adaptive diminishing smoothing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "map inference via l2 sphere linear program reformulation")
  Member "map estimation linear programming and belief propagation with convex free energies":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")
  Member "opengm a c library for discrete graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "referring expression grounding by marginalizing scene graph likelihood")
  Member "tightening lp relaxations for map using message passing":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "graph structured prediction energy networks")
  Member "a new class of upper bounds on the log partition function":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "visual semantic information pursuit a survey")
  Member "tightening fractional covering upper bounds on the partition function for high order region graphs":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "decomposition bounds for marginal map")
  Member "norm product belief propagation primal dual message passing for approximate inference":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "scalable explanation of inferences on large graphs")

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.NA(Numerical Analysis)