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 "tightening fractional covering upper bounds on the partition function for high order region graphs"):
  Abstract: In this paper we present a new approach for tightening upper bounds on the partition function. Our upper bounds are based on fractional covering bounds on the entropy function, and result in a concave program to compute these bounds and a convex program to tighten them. To solve these programs effectively for general region graphs we utilize the entropy barrier method, thus decomposing the original programs by their dual programs and solve them with dual block optimization scheme. The entropy barrier method provides an elegant framework to generalize the message-passing scheme to high-order region graph, as well as to solve the block dual steps in closed-form. This is a key for computational relevancy for large problems with thousands of regions.

Includes members:
  Member "message passing algorithms reparameterizations and splittings":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "message passing and combinatorial optimization")
  Member "convergent message passing algorithms for inference over general graphs with convex free energies":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")
  Member "convergent message passing algorithms a unifying view":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "graph structured prediction energy networks")
  Member "tightening lp relaxations for map using message passing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "graph structured prediction energy networks")
  Member "convergent propagation algorithms via oriented trees":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "lifted tree reweighted variational inference")
  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 "information inequalities for joint distributions with interpretations and applications":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "dual loomis whitney inequalities via information theory")

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)