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 "logsmooth gradient concentration and tighter runtimes for metropolized hamiltonian monte carlo"):
  Abstract: We show that the gradient norm $\|\nabla f(x)\|$ for $x \sim \exp(-f(x))$, where $f$ is strongly convex and smooth, concentrates tightly around its mean. This removes a barrier in the prior state-of-the-art analysis for the well-studied Metropolized Hamiltonian Monte Carlo (HMC) algorithm for sampling from a strongly logconcave distribution. We correspondingly demonstrate that Metropolized HMC mixes in $\tilde{O}(\kappa d)$ iterations, improving upon the $\tilde{O}(\kappa^{1.5}\sqrt{d} + \kappa d)$ runtime of (Dwivedi et. al. '18, Chen et. al. '19) by a factor $(\kappa/d)^{1/2}$ when the condition number $\kappa$ is large. Our mixing time analysis introduces several techniques which to our knowledge have not appeared in the literature and may be of independent interest, including restrictions to a nonconvex set with good conductance behavior, and a new reduction technique for boosting a constant-accuracy total variation guarantee under weak warmness assumptions. This is the first mixing time result for logconcave distributions using only first-order function information which achieves linear dependence on $\kappa$; we also give evidence that this dependence is likely to be necessary for standard Metropolized first-order methods.

Includes members:
  Member "the randomized midpoint method for log concave sampling":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "estimating normalizing constants for log concave distributions algorithms and lower bounds")
  Member "optimal convergence rate of hamiltonian monte carlo for strongly logconcave distributions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "rapid convergence of the unadjusted langevin algorithm isoperimetry suffices")
  Member "computational separations between sampling and optimization":
    also connected through other hyperedges:
      (none)
  Member "rapid convergence of the unadjusted langevin algorithm isoperimetry suffices":
    also connected through other hyperedges:
      (none)
  Member "algorithmic theory of odes and sampling from well conditioned logconcave densities":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "efficient symmetric norm regression via linear sketching")

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)