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 for symmetric rank one matrix estimation a proof of the replica formula"):
  Abstract: Factorizing low-rank matrices has many applications in machine learning and statistics. For probabilistic models in the Bayes optimal setting, a general expression for the mutual information has been proposed using heuristic statistical physics computations, and proven in few specific cases. Here, we show how to rigorously prove the conjectured formula for the symmetric rank-one case. This allows to express the minimal mean-square-error and to characterize the detectability phase transitions in a large set of estimation problems ranging from community detection to sparse PCA. We also show that for a large set of parameters, an iterative algorithm called approximate message-passing is Bayes optimal. There exists, however, a gap between what currently known polynomial algorithms can do and what is expected information theoretically. Additionally, the proof technique has an interest of its own and exploits three essential ingredients: the interpolation method introduced in statistical physics by Guerra, the analysis of the approximate message-passing algorithm and the theory of spatial coupling and threshold saturation in coding. Our approach is generic and applicable to other open problems in statistical estimation where heuristic statistical physics predictions are available.

Includes members:
  Member "threshold saturation of spatially coupled sparse superposition codes for all memoryless channels":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "compressed coding amp based decoding and analog spatial coupling")
  Member "mutual information in rank one matrix estimation":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "overlap matrix concentration in optimal bayesian inference")
  Member "phase transitions in sparse pca":
    also connected through other hyperedges:
      - Hyperedge HE-3 (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-4 (induced by source paper "the kikuchi hierarchy and tensor pca")
  Member "mmse of probabilistic low rank matrix estimation universality with respect to the output channel":
    also connected through other hyperedges:
      - Hyperedge HE-5 (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-6 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "a simple proof of maxwell saturation for coupled scalar recursions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (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-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)