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 "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods"):
  Abstract: We consider the problem of approximating partition functions for Ising models. We make use of recent tools in combinatorial optimization: the Sherali-Adams and Lasserre convex programming hierarchies, in combination with variational methods to get algorithms for calculating partition functions in these families. These techniques give new, non-trivial approximation guarantees for the partition function beyond the regime of correlation decay. They also generalize some classical results from statistical physics about the Curie-Weiss ferromagnetic Ising model, as well as provide a partition function counterpart of classical results about max-cut on dense graphs \cite{arora1995polynomial}. With this, we connect techniques from two apparently disparate research areas -- optimization and counting/partition function approximations. (i.e. \#-P type of problems). #R##N#Furthermore, we design to the best of our knowledge the first provable, convex variational methods. Though in the literature there are a host of convex versions of variational methods \cite{wainwright2003tree, wainwright2005new, heskes2006convexity, meshi2009convexifying}, they come with no guarantees (apart from some extremely special cases, like e.g. the graph has a single cycle \cite{weiss2000correctness}). We consider dense and low threshold rank graphs, and interestingly, the reason our approach works on these types of graphs is because local correlations propagate to global correlations -- completely the opposite of algorithms based on correlation decay. In the process we design novel entropy approximations based on the low-order moments of a distribution. #R##N#Our proof techniques are very simple and generic, and likely to be applicable to many other settings other than Ising models.

Includes members:
  Member "rounding sum of squares relaxations":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "convexifying the bethe free energy":
    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 "a new class of upper bounds on the log partition function":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "visual semantic information pursuit a survey")
  Member "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "efficient distance approximation for structured high dimensional distributions via learning")
  Member "correlation decay up to uniqueness in spin systems":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "rounding semidefinite programming hierarchies via global correlation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "new dependencies of hierarchies in polynomial optimization")
  Member "approximate counting via correlation decay in spin systems":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "computational transition at the uniqueness threshold":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")

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)