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 "the bethe permanent of a nonnegative matrix"):
  Abstract: It has recently been observed that the permanent of a nonnegative square matrix, i.e., of a square matrix containing only nonnegative real entries, can very well be approximated by solving a certain Bethe free energy function minimization problem with the help of the sum-product algorithm. We call the resulting approximation of the permanent the Bethe permanent. In this paper, we give reasons why this approach to approximating the permanent works well. Namely, we show that the Bethe free energy function is convex and that the sum-product algorithm finds its minimum efficiently. We then discuss the fact that the permanent is lower bounded by the Bethe permanent, and we comment on potential upper bounds on the permanent based on the Bethe permanent. We also present a combinatorial characterization of the Bethe permanent in terms of permanents of so-called lifted versions of the matrix under consideration. Moreover, we comment on possibilities to modify the Bethe permanent so that it approximates the permanent even better, and we conclude the paper with some observations and conjectures about permanent-based pseudocodewords and permanent-based kernels.

Includes members:
  Member "extropy complementary dual of entropy":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "multivariate dependence beyond shannon information")
  Member "counting in graph covers a combinatorial characterization of the bethe entropy function":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "pseudocodeword based decoding of quantum stabilizer codes")
  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 "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 "the bethe partition function of log supermodular graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "lifted hybrid variational inference")
  Member "pseudocodewords from bethe permanents":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "counting in graph covers a combinatorial characterization of the bethe entropy function")
  Member "belief propagation for weighted b matchings on arbitrary graphs and its relation to linear programs with integer solutions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "pils exploring high order neighborhoods by pattern mining and injection")
  Member "partition functions of normal factor graphs":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "codes on graphs models for elementary algebraic topology and statistical physics")

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.IT(Information Theory)