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 "discrete geometric analysis of message passing algorithm on graphs"):
  Abstract: We often encounter probability distributions given as unnormalized products of non-negative functions. The factorization structures are represented by hypergraphs called factor graphs. Such distributions appear in various fields, including statistics, artificial intelligence, statistical physics, error correcting codes, etc. Given such a distribution, computations of marginal distributions and the normalization constant are often required. However, they are computationally intractable because of their computational costs. One successful approximation method is Loopy Belief Propagation (LBP) algorithm. The focus of this thesis is an analysis of the LBP algorithm. If the factor graph is a tree, i.e. having no cycle, the algorithm gives the exact quantities. If the factor graph has cycles, however, the LBP algorithm does not give exact results and possibly exhibits oscillatory and non-convergent behaviors. The thematic question of this thesis is "How the behaviors of the LBP algorithm are affected by the discrete geometry of the factor graph?" The primary contribution of this thesis is the discovery of a formula that establishes the relation between the LBP, the Bethe free energy and the graph zeta function. This formula provides new techniques for analysis of the LBP algorithm, connecting properties of the graph and of the LBP and the Bethe free energy. We demonstrate applications of the techniques to several problems including (non) convexity of the Bethe free energy, the uniqueness and stability of the LBP fixed point. We also discuss the loop series initiated by Chertkov and Chernyak. The loop series is a subgraph expansion of the normalization constant, or partition function, and reflects the graph geometry. We investigate theoretical natures of the series. Moreover, we show a partial connection between the loop series and the graph zeta function.

Includes members:
  Member "loopy belief propagation for approximate inference an empirical study":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "analyzing differentiable fuzzy logic operators")
  Member "expectation propagation for approximate bayesian inference":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "bayesian deep learning and a probabilistic perspective of generalization")
  Member "belief optimization for binary networks a stable alternative to loopy belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lifted hybrid variational inference")
  Member "graph zeta function in the bethe free energy and loopy belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "explicit near ramanujan graphs of every degree")
  Member "approximate inference on planar graphs using loop calculus and belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "gaussian belief propagation solver for systems of linear equations":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "distributed convergence verification for gaussian belief propagation")
  Member "belief propagation and beyond for particle tracking":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximating the permanent by sampling from adaptive partitions")
  Member "polynomial linear programming with gaussian belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "distributed intelligent illumination control in the context of probabilistic graphical models")

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.DM(Discrete Mathematics)