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 "high dimensional inference with random maximum a posteriori perturbations"):
  Abstract: This paper presents a new approach, called perturb-max, for high-dimensional statistical inference that is based on applying random perturbations followed by optimization. This framework injects randomness to maximum a-posteriori (MAP) predictors by randomly perturbing the potential function for the input. A classic result from extreme value statistics asserts that perturb-max operations generate unbiased samples from the Gibbs distribution using high-dimensional perturbations. Unfortunately, the computational cost of generating so many high-dimensional random variables can be prohibitive. However, when the perturbations are of low dimension, sampling the perturb-max prediction is as efficient as MAP optimization. This paper shows that the expected value of perturb-max inference with low dimensional perturbations can be used sequentially to generate unbiased samples from the Gibbs distribution. Furthermore the expected value of the maximal perturbations is a natural bound on the entropy of such perturb-max models. A measure concentration result for perturb-max values shows that the deviation of their sampled average from its expectation decays exponentially in the number of samples, allowing effective approximation of the expectation.

Includes members:
  Member "direct optimization through arg max for discrete variational auto encoder":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "estimating gradients for discrete random variables by sampling without replacement")
  Member "approximate inference via weighted rademacher complexity":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "bounding data driven model errors in power grid analysis")
  Member "the concrete distribution a continuous relaxation of discrete random variables":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "domain decluttering simplifying images to mitigate synthetic real domain shift and improve depth estimation")
  Member "taming the curse of dimensionality discrete integration by hashing and optimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "towards efficient discrete integration via adaptive quantile queries")
  Member "on measure concentration of random maximum a posteriori perturbations":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "learning with differentiable perturbed optimizers")
  Member "optimization with parity constraints from binary codes to discrete integration":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "quantitative verification of neural networks and its security applications")
  Member "on sampling from the gibbs distribution with random maximum a posteriori perturbations":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "learning with differentiable perturbed optimizers")
  Member "map estimation linear programming and belief propagation with convex free energies":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")

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)