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 "mutual information in rank one matrix estimation"):
  Abstract: We consider the estimation of a n-dimensional vector x from the knowledge of noisy and possibility non-linear element-wise measurements of xxT, a very generic problem that contains, e.g. stochastic 2-block model, submatrix localization or the spike perturbation of random matrices. Using an interpolation method proposed by Guerra [1] and later refined by Korada and Macris [2], we prove that the Bethe mutual information (related to the Bethe free energy and conjectured to be exact by Lesieur et al. [3] on the basis of the non-rigorous cavity method) always yields an upper bound to the exact mutual information. A lower bound is also provided using a similar technique. For concreteness, we illustrate our findings on the sparse PCA problem, and observe that (a) our bounds match for a large region of parameters and (b) that there exists a phase transition in a region where the spectrum remains uninformative. While we present only the case of rank-one symmetric matrix estimation, our proof technique is readily extendable to low-rank symmetric matrix or low-rank symmetric tensor estimation.

Includes members:
  Member "phase transitions in sparse pca":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "the kikuchi hierarchy and tensor pca")
  Member "asymptotic mutual information for the two groups stochastic block model":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the kikuchi hierarchy and tensor pca")
  Member "spectral detection in the censored block model":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "spectral clustering of signed graphs via matrix power means")
  Member "mmse of probabilistic low rank matrix estimation universality with respect to the output channel":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "average case lower bounds for learning sparse mixtures robust estimation and semirandom adversaries")
  Member "information theoretically optimal sparse pca":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "decoding binary node labels from censored edge measurements phase transition and efficient recovery":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "spectral clustering of signed graphs via matrix power means")
  Member "community detection thresholds and the weak ramanujan property":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "from tree matching to sparse graph alignment")
  Member "iterative estimation of constrained rank one matrices in noise":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")

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)