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 "precise phase transition of total variation minimization"):
  Abstract: Characterizing the phase transitions of convex optimizations in recovering structured signals or data is of central importance in compressed sensing, machine learning and statistics. The phase transitions of many convex optimization signal recovery methods such as $\ell_1$ minimization and nuclear norm minimization are well understood through recent years' research. However, rigorously characterizing the phase transition of total variation (TV) minimization in recovering sparse-gradient signal is still open. In this paper, we fully characterize the phase transition curve of the TV minimization. Our proof builds on Donoho, Johnstone and Montanari's conjectured phase transition curve for the TV approximate message passing algorithm (AMP), together with the linkage between the minmax Mean Square Error of a denoising problem and the high-dimensional convex geometry for TV minimization.

Includes members:
  Member "corrupted sensing novel guarantees for separating structured signals":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "gradient descent with early stopping is provably robust to label noise for overparameterized neural networks")
  Member "living on the edge phase transitions in convex programs with random data":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on the convex geometry of blind deconvolution and matrix completion")
  Member "sharp mse bounds for proximal denoising":
    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 "guarantees of total variation minimization for signal recovery":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "living near the edge a lower bound on the phase transition of total variation minimization")
  Member "accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "living near the edge a lower bound on the phase transition of total variation minimization")
  Member "the dynamics of message passing on dense graphs with applications to compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "various thresholds for ell_1 optimization in compressed sensing":
    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 "exact matrix completion via convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")

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)