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 "primal dual rates and certificates"):
  Abstract: We propose an algorithm-independent framework to equip existing optimization methods with primal-dual certificates. Such certificates and corresponding rate of convergence guarantees are important for practitioners to diagnose progress, in particular in machine learning applications. We obtain new primal-dual convergence rates, e.g., for the Lasso as well as many L1, Elastic Net, group Lasso and TV-regularized problems. The theory applies to any norm-regularized generalized linear model. Our approach provides efficiently computable duality gaps which are globally defined, without modifying the original problems in the region of interest.

Includes members:
  Member "adding vs averaging in distributed primal dual optimization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "faster on device training using new federated momentum algorithm")
  Member "linear convergence of the randomized feasible descent method under the weak strong convexity assumption":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "stochastic distributed and federated optimization for machine learning")
  Member "distributed optimization with arbitrary local solvers":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "adaptivity of stochastic gradient methods for nonconvex optimization")
  Member "sdca without duality":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "riemannian stochastic variance reduced gradient algorithm with retraction and vector transport")
  Member "distributed mini batch sdca":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "stochastic distributed and federated optimization for machine learning")
  Member "l1 regularized distributed optimization a communication efficient primal dual framework":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "stochastic distributed and federated optimization for machine learning")
  Member "mini batch primal and dual methods for svms":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "distributed dual coordinate ascent in general tree networks and its application in federated learning")
  Member "an equivalence between the lasso and support vector machines":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "data encoding for byzantine resilient distributed optimization")

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)