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 "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.

Includes members:
  Member "the vertex sample complexity of free energy is polynomial":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective")
  Member "the ising partition function zeros and deterministic approximation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "zeros and approximations of holant polynomials on the complex plane")
  Member "approximating partition functions in constant time":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the vertex sample complexity of free energy is polynomial")
  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 "gauges loops and polynomials for partition functions of graphical models")
  Member "a new regularity lemma and faster approximation algorithms for low threshold rank graphs":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximating constraint satisfaction problems on high dimensional expanders")
  Member "sufficient conditions for convergence of the sum product algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "factorized graph representations for semi supervised learning from sparse data")

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)