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 vertex sample complexity of free energy is polynomial"
  Abstract: We study the following question: given a massive Markov random field on $n$ nodes, can a small sample from it provide a rough approximation to the free energy $\mathcal{F}_n = \log{Z_n}$? #R##N#Results in graph limit literature by Borgs, Chayes, Lov{\'a}sz, S{\'o}s, and Vesztergombi show that for Ising models on $n$ nodes and interactions of strength $\Theta(1/n)$, an $\epsilon$ approximation to $\log Z_n / n$ can be achieved by sampling a randomly induced model on $2^{O(1/\epsilon^2)}$ nodes. We show that the sampling complexity of this problem is {\em polynomial in} $1/\epsilon$. We further show a polynomial dependence on $\epsilon$ cannot be avoided. #R##N#Our results are very general as they apply to higher order Markov random fields. For Markov random fields of order $r$, we obtain an algorithm that achieves $\epsilon$ approximation using a number of samples polynomial in $r$ and $1/\epsilon$ and running time that is $2^{O(1/\epsilon^2)}$ up to polynomial factors in $r$ and $\epsilon$. For ferromagnetic Ising models, the running time is polynomial in $1/\epsilon$. #R##N#Our results are intimately connected to recent research on the regularity lemma and property testing, where the interest is in finding which properties can tested within $\epsilon$ error in time polynomial in $1/\epsilon$. In particular, our proofs build on results from a recent work by Alon, de la Vega, Kannan and Karpinski, who also introduced the notion of polynomial vertex sample complexity. Another critical ingredient of the proof is an effective bound by the authors of the paper relating the variational free energy and the free energy.

Connected through hyperedge HE-1 (induced by source paper "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective"):
  with members:
    - "the mean field approximation information inequalities algorithms and complexity"
    - "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"

Connected through hyperedge HE-2 (induced by source paper "the mean field approximation information inequalities algorithms and complexity"):
  with members:
    - "the ising partition function zeros and deterministic approximation"
    - "approximating partition functions in constant time"
    - "how to calculate partition functions using convex programming hierarchies provable bounds for variational methods"
    - "a new regularity lemma and faster approximation algorithms for low threshold rank graphs"
    - "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)