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 "distribution dependent analysis of gibbs erm principle"):
  Abstract: Gibbs-ERM learning is a natural idealized model of learning with stochastic optimization algorithms (such as Stochastic Gradient Langevin Dynamics and ---to some extent--- Stochastic Gradient Descent), while it also arises in other contexts, including PAC-Bayesian theory, and sampling mechanisms. In this work we study the excess risk suffered by a Gibbs-ERM learner that uses non-convex, regularized empirical risk with the goal to understand the interplay between the data-generating distribution and learning in large hypothesis spaces. Our main results are distribution-dependent upper bounds on several notions of excess risk. We show that, in all cases, the distribution-dependent excess risk is essentially controlled by the effective dimension $\mathrm{tr}\left(\boldsymbol{H}^{\star} (\boldsymbol{H}^{\star} + \lambda \boldsymbol{I})^{-1}\right)$ of the problem, where $\boldsymbol{H}^{\star}$ is the Hessian matrix of the risk at a local minimum. This is a well-established notion of effective dimension appearing in several previous works, including the analyses of SGD and ridge regression, but ours is the first work that brings this dimension to the analysis of learning using Gibbs densities. The distribution-dependent view we advocate here improves upon earlier results of Raginsky et al. (2017), and can yield much tighter bounds depending on the interplay between the data-generating distribution and the loss function. The first part of our analysis focuses on the localized excess risk in the vicinity of a fixed local minimizer. This result is then extended to bounds on the global excess risk, by characterizing probabilities of local minima (and their complement) under Gibbs densities, a results which might be of independent interest.

Includes members:
  Member "iterate averaging as regularization for stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient and robust algorithms for adversarial linear contextual bandits")
  Member "data dependent pac bayes priors via differential privacy":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "dissecting non vacuous generalization bounds based on the mean field approximation")
  Member "piecewise strong convexity of neural networks":
    also connected through other hyperedges:
      (none)
  Member "local optimality and generalization guarantees for the langevin algorithm via empirical metastability":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "on generalization error bounds of noisy gradient methods for non convex learning")
  Member "information theoretic analysis of generalization capability of learning algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the information bottleneck problems models connections applications and information theoretic views")
  Member "fisher rao metric geometry and complexity of neural networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "the role of invariance in spectral complexity based generalization bounds")
  Member "non convex learning via stochastic gradient langevin dynamics a nonasymptotic analysis":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "an empirical study of large batch stochastic gradient descent with structured covariance noise")
  Member "generalization bounds of sgld for non convex learning two theoretical viewpoints":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "an empirical study of large batch stochastic gradient descent with structured covariance noise")

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)