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: "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.

Connected through hyperedge HE-1 (induced by source paper "gauges loops and polynomials for partition functions of graphical models"):
  with members:
    - "the ising partition function zeros and deterministic approximation"
    - "belief propagation bethe approximation and polynomials"
    - "a generalization of permanent inequalities and applications in counting and optimization"
    - "a faster approximation algorithm for the gibbs partition function"
    - "the bethe permanent of a nonnegative matrix"
    - "counting in graph covers a combinatorial characterization of the bethe entropy function"
    - "a cluster cumulant expansion at the fixed points of belief propagation"
    - "the bethe partition function of log supermodular graphical models"

Connected through hyperedge HE-2 (induced by source paper "graphical models and belief propagation hierarchy for physics constrained network flows"):
  with members:
    - "minimum weight perfect matching via blossom belief propagation"
    - "a differential analysis of the power flow equations"
    - "solving the power flow equations a monotone operator approach"
    - "submodular functions from discrete to continous domains"
    - "natural gas flow solutions with guarantees a monotone operator theory approach"
    - "optimal compression in natural gas networks a geometric programming approach"
    - "the power of linear programming for general valued csps"
    - "tightening lp relaxations for map using message passing"

Connected through hyperedge HE-3 (induced by source paper "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective"):
  with members:
    - "the vertex sample complexity of free energy is polynomial"
    - "the mean field approximation information inequalities algorithms and complexity"
    - "a birthday repetition theorem and complexity of approximating dense csps"
    - "sub exponential approximation schemes for csps from dense to almost sparse"
    - "conditioning and covariance on caterpillars"
    - "rounding semidefinite programming hierarchies via global correlation"
    - "approximating csps with global cardinality constraints using sdp hierarchies"

Connected through hyperedge HE-4 (induced by source paper "the mean field approximation information inequalities algorithms and complexity"):
  with members:
    - "the vertex sample complexity of free energy is polynomial"
    - "the ising partition function zeros and deterministic approximation"
    - "approximating partition functions in constant time"
    - "a new regularity lemma and faster approximation algorithms for low threshold rank graphs"
    - "sufficient conditions for convergence of the sum product algorithm"

Connected through hyperedge HE-5 (induced by source paper "the vertex sample complexity of free energy is polynomial"):
  with members:
    - "approximating partition functions in constant time"
    - "entropy optimization and counting"

Connected through hyperedge HE-6 (induced by source paper "approximating partition functions in constant time"):
  with members:
    - "the ising partition function zeros and deterministic approximation"
    - "a new regularity lemma and faster approximation algorithms for low threshold rank graphs"

Connected through hyperedge HE-7 (induced by source paper "approximate maximum entropy principles via goemans williamson with applications to provable variational methods"):
  with members:
    - "rounding sum of squares relaxations"
    - "entropy optimization and counting"
    - "a new class of upper bounds on the log partition function"

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)