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 "optimal phase transitions in compressed sensing"):
  Abstract: Compressed sensing deals with efficient recovery of analog signals from linear encodings. This paper presents a statistical study of compressed sensing by modeling the input signal as an i.i.d. process with known distribution. Three classes of encoders are considered, namely optimal nonlinear, optimal linear and random linear encoders. Focusing on optimal decoders, we investigate the fundamental tradeoff between measurement rate and reconstruction fidelity gauged by error probability and noise sensitivity in the absence and presence of measurement noise, respectively. The optimal phase transition threshold is determined as a functional of the input distribution and compared to suboptimal thresholds achieved by popular reconstruction algorithms. In particular, we show that Gaussian sensing matrices incur no penalty on the phase transition threshold with respect to optimal nonlinear encoding. Our results also provide a rigorous justification of previous results based on replica heuristics in the weak-noise regime.

Includes members:
  Member "support recovery with sparsely sampled free random matrices":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "bilinear recovery using adaptive vector amp")
  Member "asymptotic analysis of map estimation via the replica method and applications to compressed sensing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "unsourced multiuser sparse regression codes achieve the symmetric mac capacity")
  Member "information theoretically optimal compressed sensing via spatial coupling and approximate message passing":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "accurate prediction of phase transitions in compressed sensing via a connection to minimax denoising":
    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 "asymptotic analysis of complex lasso via complex approximate message passing camp":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "optimal errors and phase transitions in high dimensional generalized linear models")
  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 "lower bounds for sparse recovery":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "querying a matrix through matrix vector products")
  Member "estimation in gaussian noise properties of the minimum mean square error":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "compressed coding amp based decoding and analog spatial coupling")

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)