human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding"):
  with members:
    - "sparse regression codes"
    - "the error probability of sparse superposition codes with approximate message passing decoding"
    - "spatially coupled sparse regression codes design and state evolution analysis"
    - "finite sample analysis of approximate message passing algorithms"
    - "techniques for improving the finite length performance of sparse superposition codes"
    - "approximate message passing decoder and capacity achieving sparse superposition codes"
    - "capacity achieving sparse superposition codes via approximate message passing decoding"
    - "universal sparse superposition codes with spatial coupling and gamp decoding"

Connected through hyperedge HE-2 (induced by source paper "understanding phase transitions via mutual information and mmse"):
  with members:
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "multi layer generalized linear estimation"
    - "additivity of information in multilayer networks via additive gaussian noise transforms"
    - "generalized expectation consistent signal recovery for nonlinear measurements"
    - "dynamical functional theory for compressed sensing"
    - "phase transitions optimal errors and optimality of message passing in generalized linear models"
    - "the replica symmetric prediction for compressed sensing with gaussian matrices is exact"
    - "expectation consistent approximate inference generalizations and convergence"

Connected through hyperedge HE-3 (induced by source paper "overlap matrix concentration in optimal bayesian inference"):
  with members:
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "asymptotics of map inference in deep networks"
    - "entropy and mutual information in models of deep neural networks"
    - "mutual information for low rank even order symmetric tensor factorization"
    - "the committee machine computational to statistical gaps in learning a two layers neural network"
    - "rank one matrix estimation analysis of algorithmic and information theoretic limits by the spatial coupling method"
    - "the mutual information in random linear estimation beyond i i d matrices"
    - "adaptive path interpolation for sparse systems application to a simple censored block model"

Connected through hyperedge HE-4 (induced by source paper "concentration of the matrix valued minimum mean square error in optimal bayesian inference"):
  with members:
    - "overlap matrix concentration in optimal bayesian inference"
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "asymptotics of map inference in deep networks"
    - "entropy and mutual information in models of deep neural networks"
    - "mutual information for low rank even order symmetric tensor factorization"
    - "the committee machine computational to statistical gaps in learning a two layers neural network"
    - "rank one matrix estimation analysis of algorithmic and information theoretic limits by the spatial coupling method"
    - "the mutual information in random linear estimation beyond i i d matrices"

Connected through hyperedge HE-5 (induced by source paper "the kikuchi hierarchy and tensor pca"):
  with members:
    - "the power of sum of squares for detecting hidden structures"
    - "a nearly tight sum of squares lower bound for the planted clique problem"
    - "sum of squares certificates for maxima of random tensors on the sphere"
    - "multiplicative approximations for polynomial optimization over the unit sphere"
    - "strongly refuting random csps below the spectral threshold"
    - "phase transitions in sparse pca"
    - "how to refute a random csp"
    - "asymptotic mutual information for the two groups stochastic block model"

Connected through hyperedge HE-6 (induced by source paper "0 1 phase transitions in sparse spiked matrix estimation"):
  with members:
    - "mutual information for low rank even order symmetric tensor factorization"
    - "finite sample analysis of approximate message passing algorithms"
    - "reducibility and computational lower bounds for problems with planted sparse structure"
    - "estimation in the spiked wigner model a short proof of the replica formula"
    - "the layered structure of tensor estimation and its mutual information"
    - "mutual information in rank one matrix estimation"
    - "sum of squares lower bounds for sparse pca"
    - "information theoretically optimal sparse pca"

Connected through hyperedge HE-7 (induced by source paper "mutual information in community detection with covariate information and correlated networks"):
  with members:
    - "the geometry of community detection via the mmse matrix"
    - "community detection with side information exact recovery under the stochastic block model"
    - "information theoretic thresholds from the cavity method"
    - "the computer science and physics of community detection landscapes phase transitions and hardness"
    - "structure and inference in annotated networks"
    - "mutual information in rank one matrix estimation"
    - "phase transitions in semisupervised clustering of sparse networks"
    - "phase transitions in community detection a solvable toy model"

Connected through hyperedge HE-8 (induced by source paper "mutual information for low rank even order symmetric tensor factorization"):
  with members:
    - "overlap matrix concentration in optimal bayesian inference"
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "estimation in the spiked wigner model a short proof of the replica formula"
    - "the layered structure of tensor estimation and its mutual information"
    - "mutual information in rank one matrix estimation"
    - "asymptotic mutual information for the two groups stochastic block model"
    - "a statistical model for tensor pca"

Question: Please tell me which class the center node 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)