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 "on the chain rule optimal transport distance"):
  Abstract: We define a novel class of distances between statistical multivariate distributions by solving an optimal transportation problem on their marginal densities with respect to a ground distance defined on their conditional densities. By using the chain rule factorization of probabilities, we show how to perform optimal transport on a ground space being an information-geometric manifold of conditional probabilities. We prove that this new distance is a metric whenever the chosen ground distance is a metric. Our distance generalizes both the Wasserstein distances between point sets and a recently introduced metric distance between statistical mixtures. As a first application of this Chain Rule Optimal Transport (CROT) distance, we show that the ground distance between statistical mixtures is upper bounded by this optimal transport distance, whenever the ground distance is joint convex. We report on our experiments which quantify the tightness of the CROT distance for the total variation distance and a square root generalization of the Jensen-Shannon divergence between mixtures.

Includes members:
  Member "guaranteed deterministic bounds on the total variation distance between univariate mixtures":
    also connected through other hyperedges:
      (none)
  Member "monte carlo information geometry the dually flat case":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "on the jensen shannon symmetrization of distances relying on abstract means")
  Member "on w mixtures finite convex combinations of prescribed component distributions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "monte carlo information geometry the dually flat case")
  Member "fashion mnist a novel image dataset for benchmarking machine learning algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "guaranteed bounds on information theoretic measures of univariate mixtures using piecewise log sum exp inequalities":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a generalization of the α divergences based on comparable and distinct weighted means")
  Member "on the chi square and higher order chi distances for approximating f divergences":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the jensen shannon symmetrization of distances relying on abstract means")
  Member "generalized bhattacharyya and chernoff upper bounds on bayes error using quasi arithmetic means":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "the alpha divergences associated with a pair of strictly comparable quasi arithmetic means")
  Member "a closed form expression for the sharma mittal entropy of exponential families":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "q vae for disentangled representation learning and latent dynamical systems")

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)