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 "nonconvex sampling with the metropolis adjusted langevin algorithm"):
  Abstract: The Langevin Markov chain algorithms are widely deployed methods to sample from distributions in challenging high-dimensional and non-convex statistics and machine learning applications. Despite this, current bounds for the Langevin algorithms are slower than those of competing algorithms in many important situations, for instance when sampling from weakly log-concave distributions, or when sampling or optimizing non-convex log-densities. In this paper, we obtain improved bounds in many of these situations, showing that the Metropolis-adjusted Langevin algorithm (MALA) is faster than the best bounds for its competitor algorithms when the target distribution satisfies weak third- and fourth- order regularity properties associated with the input data. In many settings, our regularity conditions are weaker than the usual Euclidean operator norm regularity properties, allowing us to show faster bounds for a much larger class of distributions than would be possible with the usual Euclidean operator norm approach, including in statistics and machine learning applications where the data satisfy a certain incoherence condition. In particular, we show that using our regularity conditions one can obtain faster bounds for applications which include sampling problems in Bayesian logistic regression with weakly convex priors, and the nonconvex optimization problem of learning linear classifiers with zero-one loss functions. #R##N#Our main technical contribution in this paper is our analysis of the Metropolis acceptance probability of MALA in terms of its "energy-conservation error," and our bound for this error in terms of third- and fourth- order regularity conditions. Our combination of this higher-order analysis of the energy conservation error with the conductance method is key to obtaining bounds which have a sub-linear dependence on the dimension $d$ in the non-strongly logconcave setting.

Includes members:
  Member "online sampling from log concave distributions":
    also connected through other hyperedges:
      (none)
  Member "dimensionally tight running time bounds for second order hamiltonian monte carlo":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "algorithmic theory of odes and sampling from well conditioned logconcave densities")
  Member "dimensionally tight bounds for second order hamiltonian monte carlo":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "rapid convergence of the unadjusted langevin algorithm isoperimetry suffices")
  Member "non convex learning via stochastic gradient langevin dynamics a nonasymptotic analysis":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "an empirical study of large batch stochastic gradient descent with structured covariance noise")
  Member "a hitting time analysis of stochastic gradient langevin dynamics":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "efficient active learning of sparse halfspaces with arbitrary bounded noise")
  Member "convergence rate of riemannian hamiltonian monte carlo and faster polytope volume computation":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "strong self concordance and sampling")
  Member "efficient learning of linear separators under bounded noise":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "efficient active learning of sparse halfspaces with arbitrary bounded 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.DS(Data Structures and Algorithms)