human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "chaining meets chain rule multilevel entropic regularization and training of neural nets"):
  with members:
    - "tightening mutual information based bounds on generalization error"
    - "data dependent pac bayes priors via differential privacy"
    - "generalization error bounds for noisy iterative algorithms"
    - "chaining mutual information and tightening generalization bounds"
    - "representing smooth functions as compositions of near identity functions with implications for deep network optimization"
    - "information theoretic analysis of generalization capability of learning algorithms"
    - "non convex learning via stochastic gradient langevin dynamics a nonasymptotic analysis"
    - "computing nonvacuous generalization bounds for deep stochastic neural networks with many more parameters than training data"

Connected through hyperedge HE-2 (induced by source paper "efron stein pac bayesian inequalities"):
  with members:
    - "pac bayes un expected bernstein inequality"
    - "policy optimization via importance sampling"
    - "a tight excess risk bound via a unified pac bayesian rademacher shtarkov mdl complexity"
    - "computing nonvacuous generalization bounds for deep stochastic neural networks with many more parameters than training data"
    - "a pac bayesian approach to spectrally normalized margin bounds for neural networks"
    - "a strongly quasiconvex pac bayesian bound"
    - "pac bayesian inequalities for martingales"
    - "a note on the pac bayesian theorem"

Question: Please tell me which class the center node 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)