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: "the mean field approximation information inequalities algorithms and complexity"
  Abstract: The mean field approximation to the Ising model is a canonical variational tool that is used for analysis and inference in Ising models. We provide a simple and optimal bound for the KL error of the mean field approximation for Ising models on general graphs, and extend it to higher order Markov random fields. Our bound improves on previous bounds obtained in work in the graph limit literature by Borgs, Chayes, Lov\'asz, S\'os, and Vesztergombi and another recent work by Basak and Mukherjee. Our bound is tight up to lower order terms. Building on the methods used to prove the bound, along with techniques from combinatorics and optimization, we study the algorithmic problem of estimating the (variational) free energy for Ising models and general Markov random fields. For a graph $G$ on $n$ vertices and interaction matrix $J$ with Frobenius norm $\| J \|_F$, we provide algorithms that approximate the free energy within an additive error of $\epsilon n \|J\|_F$ in time $\exp(poly(1/\epsilon))$. We also show that approximation within $(n \|J\|_F)^{1-\delta}$ is NP-hard for every $\delta > 0$. Finally, we provide more efficient approximation algorithms, which find the optimal mean field approximation, for ferromagnetic Ising models and for Ising models satisfying Dobrushin's condition.

Connected through hyperedge HE-1 (induced by source paper "spectral approximate inference"):
  with members:
    - "the ising partition function zeros and deterministic approximation"
    - "convergence of mcmc and loopy bp in the tree uniqueness region for the hard core model"
    - "variable elimination in the fourier domain"
    - "inapproximability for antiferromagnetic spin systems in the tree non uniqueness region"
    - "a new class of upper bounds on the log partition function"
    - "approximation algorithms for two state anti ferromagnetic spin systems on bounded degree graphs"
    - "correlation decay up to uniqueness in spin systems"

Connected through hyperedge HE-2 (induced by source paper "fast convergence of belief propagation to global optima beyond correlation decay"):
  with members:
    - "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective"
    - "belief optimization for binary networks a stable alternative to loopy belief propagation"
    - "bethe bounds and approximating the global optimum"
    - "the bethe partition function of log supermodular graphical models"
    - "the dynamics of message passing on dense graphs with applications to compressed sensing"
    - "sufficient conditions for convergence of the sum product algorithm"

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"
    - "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods"
    - "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"

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)