human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "approximating the permanent with belief propagation"
  Abstract: This work describes a method of approximating matrix per- manents efficiently using belief propagation. We formulate aprobability distribution whose partition function is exactly the permanent, then use Bethe free energy to approximate this partition function. After deriving some speedups to standard belief propagation, the resulting algorithm requires (n 2 ) time per iteration. Finally, we demonstrate the advantages of using this approximation.

Connected through hyperedge HE-1 (induced by source paper "approximating the permanent by sampling from adaptive partitions"):
  with members:
    - "a tight analysis of bethe approximation for permanent"
    - "belief propagation and beyond for particle tracking"

Connected through hyperedge HE-2 (induced by source paper "a tight analysis of bethe approximation for permanent"):
  with members:
    - "log concave polynomials i entropy and a deterministic approximation algorithm for counting bases of matroids"
    - "approximate profile maximum likelihood"
    - "belief propagation bethe approximation and polynomials"
    - "approximating the permanent of a random matrix with vanishing mean"
    - "a generalization of permanent inequalities and applications in counting and optimization"
    - "nash social welfare matrix permanent and stable polynomials"
    - "the bethe permanent of a nonnegative matrix"
    - "approximating the permanent with fractional belief propagation"

Connected through hyperedge HE-3 (induced by source paper "improved lower bounds on the size of balls over permutations with the infinity metric"):
  with members:
    - "proof of a conjecture of klove on permutation codes under the chebychev distance"
    - "limited magnitude error correcting gray codes for rank modulation"
    - "compression in the space of permutations"
    - "new bounds for permutation codes in ulam metric"
    - "the bethe permanent of a nonnegative matrix"
    - "systematic error correcting codes for rank modulation"
    - "systematic codes for rank modulation"
    - "error correction in flash memories via codes in the ulam metric"

Connected through hyperedge HE-4 (induced by source paper "multiple scan data association by convex variational inference"):
  with members:
    - "a scalable algorithm for tracking an unknown number of targets using multiple sensors"
    - "marginal multi bernoulli filters rfs derivation of mht jipda and association based member"
    - "an efficient variational approximation of the best fitting multi bernoulli filter"
    - "approximate evaluation of marginal association probabilities with belief propagation"
    - "loopy belief propagation for approximate inference an empirical study"
    - "the bethe permanent of a nonnegative matrix"
    - "a new class of upper bounds on the log partition function"
    - "approximating the permanent with fractional belief propagation"

Connected through hyperedge HE-5 (induced by source paper "message passing and combinatorial optimization"):
  with members:
    - "augmentative message passing for traveling salesman problem and graph partitioning"
    - "perturbed message passing for constraint satisfaction problems"
    - "revisiting algebra and complexity of inference in graphical models"
    - "on map inference by mwss on perfect graphs"
    - "loopy belief propagation for approximate inference an empirical study"
    - "graphical models for game theory"
    - "message passing algorithms reparameterizations and splittings"
    - "the bethe permanent of a nonnegative matrix"

Connected through hyperedge HE-6 (induced by source paper "bounding the bethe and the degree m bethe permanents"):
  with members:
    - "hierarchical and high girth qc ldpc codes"
    - "the bethe permanent of a nonnegative matrix"
    - "design of multiple edge protographs for qc ldpc codes avoiding short inevitable cycles"
    - "bounds on the minimum distance of punctured quasi cyclic ldpc codes"
    - "quasi cyclic ldpc codes influence of proto and tanner graph structure on minimum hamming distance upper bounds"
    - "the bethe partition function of log supermodular graphical models"
    - "computing the permanent with belief propagation"
    - "absdet pseudo codewords and perm pseudo codewords definitions and properties"

Connected through hyperedge HE-7 (induced by source paper "marginal multi bernoulli filters rfs derivation of mht jipda and association based member"):
  with members:
    - "an efficient variational approximation of the best fitting multi bernoulli filter"
    - "approximate evaluation of marginal association probabilities with belief propagation"
    - "the bethe permanent of a nonnegative matrix"
    - "hybrid poisson and multi bernoulli filters"
    - "graphical model approximations of random finite set filters"
    - "belief propagation and beyond for particle tracking"

Connected through hyperedge HE-8 (induced by source paper "bethe learning of conditional random fields via map decoding"):
  with members:
    - "learning graphical model parameters with approximate marginal inference"
    - "the bethe permanent of a nonnegative matrix"
    - "learning graph matching"
    - "sufficient conditions for convergence of the sum product algorithm"

Question: Please tell me which class the center node 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)