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 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.

Connected through hyperedge HE-1 (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-2 (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-3 (induced by source paper "computational hardness of certifying bounds on constrained pca problems"):
  with members:
    - "mean field approximation convex hierarchies and the optimality of correlation rounding a unified perspective"
    - "heterogeneous multireference alignment a single pass approach"
    - "community detection in hypergraphs spiked tensor models and sum of squares"
    - "the lov asz theta function for random regular graphs and community detection in the hard regime"
    - "the power of sum of squares for detecting hidden structures"
    - "bayesian estimation from few samples community detection and related problems"
    - "sum of squares lower bounds for refuting any csp"
    - "a nearly tight sum of squares lower bound for the planted clique problem"

Connected through hyperedge HE-4 (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 for symmetric rank one matrix estimation a proof of the replica formula"
    - "sum of squares lower bounds for sparse pca"
    - "information theoretically optimal sparse pca"

Connected through hyperedge HE-5 (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 for symmetric rank one matrix estimation a proof of the replica formula"
    - "phase transitions in semisupervised clustering of sparse networks"
    - "phase transitions in community detection a solvable toy model"

Connected through hyperedge HE-6 (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 for symmetric rank one matrix estimation a proof of the replica formula"
    - "asymptotic mutual information for the two groups stochastic block model"
    - "a statistical model for tensor pca"

Connected through hyperedge HE-7 (induced by source paper "the geometry of community detection via the mmse matrix"):
  with members:
    - "additivity of information in multilayer networks via additive gaussian noise transforms"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "hessian and concavity of mutual information differential entropy and entropy power in linear vector gaussian channels"
    - "mutual information and minimum mean square error in gaussian channels"

Connected through hyperedge HE-8 (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 for symmetric rank one matrix estimation a proof of the replica formula"
    - "phase transitions in sparse pca"
    - "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"

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)