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 "living near the edge a lower bound on the phase transition of total variation minimization"):
  Abstract: This work is about the total variation (TV) minimization which is used for recovering gradient-sparse signals from compressed measurements. Recent studies indicate that TV minimization exhibits a phase transition behavior from failure to success as the number of measurements increases. In fact, in large dimensions, TV minimization succeeds in recovering the gradient-sparse signal with high probability when the number of measurements exceeds a certain threshold; otherwise, it fails almost certainly. Obtaining a closed-form expression that approximates this threshold is a major challenge in this field and has not been appropriately addressed yet. In this work, we derive a tight lower-bound on this threshold in case of any random measurement matrix whose null space is distributed uniformly with respect to the Haar measure. In contrast to the conventional TV phase transition results that depend on the simple gradient-sparsity level, our bound is highly affected by generalized notions of gradient-sparsity. Our proposed bound is very close to the true phase transition of TV minimization confirmed by simulation results.

Includes members:
  Member "on the error in phase transition computations for compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "improved recovery of analysis sparse vectors in presence of prior information")
  Member "sample complexity of total variation minimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "improved recovery of analysis sparse vectors in presence of prior information")
  Member "total variation minimization in compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "ell 1 analysis minimization and generalized co sparsity when does recovery succeed":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "precise phase transition of total variation minimization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "convex recovery of a structured signal from independent random linear measurements":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "robust analysis l1 recovery from gaussian measurements and total variation minimization":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "compressed sensing with 1d total variation breaking sample complexity barriers via non uniform recovery")
  Member "corrupted sensing novel guarantees for separating structured signals":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "gradient descent with early stopping is provably robust to label noise for overparameterized neural networks")

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)