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 "the randomized midpoint method for log concave sampling"):
  Abstract: Sampling from log-concave distributions is a well researched problem that has many applications in statistics and machine learning. We study the distributions of the form $p^{*}\propto\exp(-f(x))$, where $f:\mathbb{R}^{d}\rightarrow\mathbb{R}$ has an $L$-Lipschitz gradient and is $m$-strongly convex. In our paper, we propose a Markov chain Monte Carlo (MCMC) algorithm based on the underdamped Langevin diffusion (ULD). It can achieve $\epsilon\cdot D$ error (in 2-Wasserstein distance) in $\tilde{O}\left(\kappa^{7/6}/\epsilon^{1/3}+\kappa/\epsilon^{2/3}\right)$ steps, where $D\overset{\mathrm{def}}{=}\sqrt{\frac{d}{m}}$ is the effective diameter of the problem and $\kappa\overset{\mathrm{def}}{=}\frac{L}{m}$ is the condition number. Our algorithm performs significantly faster than the previously best known algorithm for solving this problem, which requires $\tilde{O}\left(\kappa^{1.5}/\epsilon\right)$ steps. Moreover, our algorithm can be easily parallelized to require only $O(\kappa\log\frac{1}{\epsilon})$ parallel steps. #R##N#To solve the sampling problem, we propose a new framework to discretize stochastic differential equations. We apply this framework to discretize and simulate ULD, which converges to the target distribution $p^{*}$. The framework can be used to solve not only the log-concave sampling problem, but any problem that involves simulating (stochastic) differential equations.

Includes members:
  Member "faster algorithms for polytope rounding sampling and volume computation via a sublinear ball walk":
    also connected through other hyperedges:
      (none)
  Member "optimal convergence rate of hamiltonian monte carlo for strongly logconcave distributions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "logsmooth gradient concentration and tighter runtimes for metropolized hamiltonian monte carlo")
  Member "algorithmic theory of odes and sampling from well conditioned logconcave densities":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "logsmooth gradient concentration and tighter runtimes for metropolized hamiltonian monte carlo")
  Member "dimensionally tight bounds for second order hamiltonian monte carlo":
    also connected through other hyperedges:
      - Hyperedge HE-3 (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-4 (induced by source paper "an empirical study of large batch stochastic gradient descent with structured covariance noise")
  Member "a tutorial on thompson sampling":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "effective diversity in population based reinforcement learning")
  Member "convergence rate of riemannian hamiltonian monte carlo and faster polytope volume computation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "strong self concordance and sampling")
  Member "geodesic walks in polytopes":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "on the approximability of weighted model integration on dnf structures")

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)