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 "monte carlo information geometry the dually flat case"):
  Abstract: Exponential families and mixture families are parametric probability models that can be geometrically studied as smooth statistical manifolds with respect to any statistical divergence like the Kullback-Leibler (KL) divergence or the Hellinger divergence. When equipping a statistical manifold with the KL divergence, the induced manifold structure is dually flat, and the KL divergence between distributions amounts to an equivalent Bregman divergence on their corresponding parameters. In practice, the corresponding Bregman generators of mixture/exponential families require to perform definite integral calculus that can either be too time-consuming (for exponentially large discrete support case) or even do not admit closed-form formula (for continuous support case). In these cases, the dually flat construction remains theoretical and cannot be used by information-geometric algorithms. To bypass this problem, we consider performing stochastic Monte Carlo (MC) estimation of those integral-based mixture/exponential family Bregman generators. We show that, under natural assumptions, these MC generators are almost surely Bregman generators. We define a series of dually flat information geometries, termed Monte Carlo Information Geometries, that increasingly-finely approximate the untractable geometry. The advantage of this MCIG is that it allows a practical use of the Bregman algorithmic toolbox on a wide range of probability distribution families. We demonstrate our approach with a clustering task on a mixture family manifold.

Includes members:
  Member "on w mixtures finite convex combinations of prescribed component distributions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the chain rule optimal transport distance")
  Member "fast exact k means k medians and bregman divergence clustering in 1d":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "polynomial algorithms for p dispersion problems in a 2d pareto front")
  Member "guaranteed bounds on information theoretic measures of univariate mixtures using piecewise log sum exp inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a generalization of the α divergences based on comparable and distinct weighted means")
  Member "optimal interval clustering application to bregman clustering and statistical mixture learning":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the jensen shannon symmetrization of distances relying on abstract means")
  Member "the burbea rao and bhattacharyya centroids":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the alpha divergences associated with a pair of strictly comparable quasi arithmetic means")
  Member "a family of statistical symmetric divergences based on jensen s inequality":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "explain graph neural networks to understand weighted graph features in node classification")
  Member "statistical exponential families a digest with flash cards":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the jensen shannon symmetrization of distances relying on abstract means")

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)