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: "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.

Connected through hyperedge HE-1 (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"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "strongly refuting random csps below the spectral threshold"
    - "how to refute a random csp"
    - "asymptotic mutual information for the two groups stochastic block model"

Connected through hyperedge HE-2 (induced by source paper "the error probability of sparse superposition codes with approximate message passing decoding"):
  with members:
    - "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"
    - "threshold saturation of spatially coupled sparse superposition codes for all memoryless channels"
    - "proof of threshold saturation for spatially coupled sparse superposition codes"
    - "information theoretically optimal sparse pca"
    - "replica analysis and approximate message passing decoder for superposition codes"

Connected through hyperedge HE-3 (induced by source paper "mutual information for the stochastic block model by the adaptive interpolation method"):
  with members:
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "adaptive path interpolation for sparse systems application to a simple censored block model"
    - "information theoretic thresholds from the cavity method"
    - "the layered structure of tensor estimation and its mutual information"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "spectral redemption in clustering sparse networks"

Connected through hyperedge HE-4 (induced by source paper "message passing algorithms for synchronization problems over compact groups"):
  with members:
    - "finite sample analysis of approximate message passing algorithms"
    - "the projected power method an efficient algorithm for joint alignment from pairwise differences"
    - "mutual information in rank one matrix estimation"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "non unique games over compact groups and orientation estimation in cryo em"
    - "mmse of probabilistic low rank matrix estimation universality with respect to the output channel"
    - "semidefinite programs on sparse random graphs and their application to community detection"
    - "information theoretically optimal sparse pca"

Connected through hyperedge HE-5 (induced by source paper "estimation in the spiked wigner model a short proof of the replica formula"):
  with members:
    - "optimal errors and phase transitions in high dimensional generalized linear models"
    - "the stochastic interpolation method a simple scheme to prove replica formulas in bayesian inference"
    - "the layered structure of tensor estimation and its mutual information"
    - "phase transitions optimal errors and optimality of message passing in generalized linear models"
    - "mutual information in rank one matrix estimation"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "a statistical model for tensor pca"

Connected through hyperedge HE-6 (induced by source paper "statistical physics and information theory perspectives on linear inverse problems"):
  with members:
    - "approximate message passing decoder and capacity achieving sparse superposition codes"
    - "approximate message passing algorithm with universal denoising and gaussian mixture learning"
    - "performance trade offs in multi processor approximate message passing"
    - "multi processor approximate message passing using lossy compression"
    - "compressive imaging via approximate message passing with image denoising"
    - "improving m sbl for joint sparse recovery using a subspace penalty"
    - "mismatched estimation in large linear systems"
    - "two part reconstruction with noisy sudocodes"

Connected through hyperedge HE-7 (induced by source paper "performance limits for noisy multimeasurement vector problems"):
  with members:
    - "approximate message passing decoder and capacity achieving sparse superposition codes"
    - "the replica symmetric prediction for compressed sensing with gaussian matrices is exact"
    - "the mutual information in random linear estimation"
    - "improving m sbl for joint sparse recovery using a subspace penalty"
    - "efficient high dimensional inference in the multiple measurement vector problem"
    - "performance regions in compressed sensing from noisy measurements"
    - "subspace methods for joint sparse recovery"
    - "measurement bounds for sparse signal ensembles via graphical models"

Connected through hyperedge HE-8 (induced by source paper "mutual information for symmetric rank one matrix estimation a proof of the replica formula"):
  with members:
    - "threshold saturation of spatially coupled sparse superposition codes for all memoryless channels"
    - "mutual information in rank one matrix estimation"
    - "asymptotic mutual information for the two groups stochastic block model"
    - "mmse of probabilistic low rank matrix estimation universality with respect to the output channel"
    - "information theoretically optimal sparse pca"
    - "a simple proof of maxwell saturation for coupled scalar recursions"
    - "iterative estimation of constrained rank one matrices in noise"
    - "threshold saturation via spatial coupling why convolutional ldpc ensembles perform so well over the bec"

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)