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 "phase transitions in sparse pca"):
  Abstract: We study optimal estimation for sparse principal component analysis when the number of non-zero elements is small but on the same order as the dimension of the data. We employ approximate message passing (AMP) algorithm and its state evolution to analyze what is the information theoretically minimal mean-squared error and the one achieved by AMP in the limit of large sizes. For a special case of rank one and large enough density of non-zeros Deshpande and Montanari [1] proved that AMP is asymptotically optimal. We show that both for low density and for large rank the problem undergoes a series of phase transitions suggesting existence of a region of parameters where estimation is information theoretically possible, but AMP (and presumably every other polynomial algorithm) fails. The analysis of the large rank limit is particularly instructive.

Includes members:
  Member "phase transitions and sample complexity in bayes optimal matrix factorization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "information theoretically optimal sparse pca":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "iterative estimation of constrained rank one matrices in noise":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "information theoretically optimal compressed sensing via spatial coupling and approximate message passing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "optimal solutions for sparse principal component analysis":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a unified framework for data poisoning attack to graph based semi supervised learning")

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)