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 "sharp support recovery from noisy random measurements by l1 minimization"):
  Abstract: In this paper, we investigate the theoretical guarantees of penalized $\lun$ minimization (also called Basis Pursuit Denoising or Lasso) in terms of sparsity pattern recovery (support and sign consistency) from noisy measurements with non-necessarily random noise, when the sensing operator belongs to the Gaussian ensemble (i.e. random design matrix with i.i.d. Gaussian entries). More precisely, we derive sharp non-asymptotic bounds on the sparsity level and (minimal) signal-to-noise ratio that ensure support identification for most signals and most Gaussian sensing matrices by solving the Lasso problem with an appropriately chosen regularization parameter. Our first purpose is to establish conditions allowing exact sparsity pattern recovery when the signal is strictly sparse. Then, these conditions are extended to cover the compressible or nearly sparse case. In these two results, the role of the minimal signal-to-noise ratio is crucial. Our third main result gets rid of this assumption in the strictly sparse case, but this time, the Lasso allows only partial recovery of the support. We also provide in this case a sharp $\ell_2$-consistency result on the coefficient vector. The results of the present work have several distinctive features compared to previous ones. One of them is that the leading constants involved in all the bounds are sharp and explicit. This is illustrated by some numerical experiments where it is indeed shown that the sharp sparsity level threshold identified by our theoretical results below which sparsistency of the Lasso is guaranteed meets that empirically observed.

Includes members:
  Member "approximate sparsity pattern recovery information theoretic lower bounds":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "understanding phase transitions via mutual information and mmse")
  Member "information theoretic bounds for compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "random access for massive machine type communications")
  Member "necessary and sufficient conditions for sparsity pattern recovery":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "harmless interpolation of noisy data in regression")
  Member "an estimation theoretic approach for sparsity pattern recovery in the noisy setting":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "sub linear time support recovery for compressed sensing using sparse graph codes")
  Member "sharp sufficient conditions on exact sparsity pattern recovery":
    also connected through other hyperedges:
      (none)
  Member "thresholded basis pursuit an lp algorithm for achieving optimal support recovery for sparse and approximately sparse signals from noisy random measurements":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "asymptotic analysis of map estimation via the replica method and applications to compressed sensing")
  Member "shannon theoretic limits on noisy compressive sampling":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "information theoretic lower bounds for compressive sensing with generative models")
  Member "consistency of the group lasso and multiple kernel learning":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "joint user selection and precoding in multiuser mimo systems via group lasso")

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.IT(Information Theory)