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 "gauges loops and polynomials for partition functions of graphical models"):
  Abstract: Graphical models (GM) represent multivariate and generally not normalized probability distributions. Computing the normalization factor, called the partition function (PF), is the main inference challenge relevant to multiple statistical and optimization applications. The problem is of an exponential complexity with respect to the number of variables. In this manuscript, aimed at approximating the PF, we consider Multi-Graph Models (MGMs) where binary variables and multivariable factors are associated with edges and nodes, respectively, of an undirected multi-graph. We suggest a new methodology for analysis and computations that combines the Gauge Function (GF) technique with the technique from the field of real stable polynomials. We show that the GF, representing a single-out term in a finite sum expression for the PF which achieves extremum at the so-called Belief-Propagation (BP) gauge, has a natural polynomial representation in terms of gauges/variables associated with edges of the multi-graph. Moreover, GF can be used to recover the PF through a sequence of transformations allowing appealing algebraic and graphical interpretations. Algebraically, one step in the sequence consists in application of a differential operator over gauges associated with an edge. Graphically, the sequence is interpreted as a repetitive elimination/contraction of edges resulting in MGMs on decreasing in size (number of edges) graphs with the same PF as in the original MGM. Even though complexity of computing factors in the sequence of derived MGMs and respective GFs grow exponentially with the number of eliminated edges, polynomials associated with the new factors remain bi-stable if the original factors have this property. Moreover, we show that BP estimations in the sequence do not decrease, each low-bounding the PF.

Includes members:
  Member "the ising partition function zeros and deterministic approximation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "zeros and approximations of holant polynomials on the complex plane")
  Member "belief propagation bethe approximation and polynomials":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a tight analysis of bethe approximation for permanent")
  Member "a generalization of permanent inequalities and applications in counting and optimization":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a tight analysis of bethe approximation for permanent")
  Member "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "graphical models and belief propagation hierarchy for physics constrained network flows")
  Member "a faster approximation algorithm for the gibbs partition function":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "fast sampling and counting k sat solutions in the local lemma regime")
  Member "the bethe permanent of a nonnegative matrix":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "a tight analysis of bethe approximation for permanent")
  Member "counting in graph covers a combinatorial characterization of the bethe entropy function":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "pseudocodeword based decoding of quantum stabilizer codes")
  Member "a cluster cumulant expansion at the fixed points of belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "message passing and combinatorial optimization")

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)