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 "differentially private empirical risk minimization with sparsity inducing norms"):
  Abstract: Differential privacy is concerned about the prediction quality while measuring the privacy impact on individuals whose information is contained in the data. We consider differentially private risk minimization problems with regularizers that induce structured sparsity. These regularizers are known to be convex but they are often non-differentiable. We analyze the standard differentially private algorithms, such as output perturbation, Frank-Wolfe and objective perturbation. Output perturbation is a differentially private algorithm that is known to perform well for minimizing risks that are strongly convex. Previous works have derived excess risk bounds that are independent of the dimensionality. In this paper, we assume a particular class of convex but non-smooth regularizers that induce structured sparsity and loss functions for generalized linear models. We also consider differentially private Frank-Wolfe algorithms to optimize the dual of the risk minimization problem. We derive excess risk bounds for both these algorithms. Both the bounds depend on the Gaussian width of the unit ball of the dual norm. We also show that objective perturbation of the risk minimization problems is equivalent to the output perturbation of a dual optimization problem. This is the first work that analyzes the dual optimization problems of risk minimization problems in the context of differential privacy.

Includes members:
  Member "differentially private empirical risk minimization revisited faster and more general":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "input perturbation a new paradigm between central and local differential privacy")
  Member "efficient private erm for smooth objectives":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "private and communication efficient edge learning a sparse differential gaussian masking distributed sgd approach")
  Member "bolt on differential privacy for scalable stochastic gradient descent based analytics":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "guidelines for implementing and auditing differentially private systems")
  Member "private empirical risk minimization beyond the worst case the effect of the constraint set geometry":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "privately learning markov random fields")
  Member "calibrating data to sensitivity in private data analysis":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "locally private hypothesis selection")
  Member "learning with submodular functions a convex optimization perspective":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "online non monotone dr submodular maximization")
  Member "structured sparsity inducing norms through submodular functions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "safe screening for the generalized conditional gradient method")
  Member "differentially private empirical risk minimization":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "scaffold stochastic controlled averaging for federated learning")

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)