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: "non negative principal component analysis message passing algorithms and sharp asymptotics"
  Abstract: Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional knowledge on the principal vector? We study the case in which the principal vector is known to lie in the positive orthant. Similar constraints arise in a number of applications, ranging from analysis of gene expression data to spike sorting in neural signal processing. #R##N#In the unconstrained case, the estimation performances of PCA has been precisely characterized using random matrix theory, under a statistical model known as the `spiked model.' It is known that the estimation error undergoes a phase transition as the signal-to-noise ratio crosses a certain threshold. Unfortunately, tools from random matrix theory have no bearing on the constrained problem. Despite this challenge, we develop an analogous characterization in the constrained case, within a one-spike model. #R##N#In particular: $(i)$~We prove that the estimation error undergoes a similar phase transition, albeit at a different threshold in signal-to-noise ratio that we determine exactly; $(ii)$~We prove that --unlike in the unconstrained case-- estimation error depends on the spike vector, and characterize the least favorable vectors; $(iii)$~We show that a non-negative principal component can be approximately computed --under the spiked model-- in nearly linear time. This despite the fact that the problem is non-convex and, in general, NP-hard to solve exactly.

Connected through hyperedge HE-1 (induced by source paper "spectral method for phase retrieval an expectation propagation perspective"):
  with members:
    - "optimal spectral initialization for signal recovery with applications to phase retrieval"
    - "expectation propagation for approximate inference free probability framework"
    - "optimization based amp for phase retrieval the impact of initialization and ell_2 regularization"
    - "rigorous dynamics of expectation propagation based signal recovery from unitarily invariant measurements"
    - "generalized expectation consistent signal recovery for nonlinear measurements"
    - "expectation consistent approximate inference generalizations and convergence"
    - "vector approximate message passing for the generalized linear model"
    - "analysis of regularized ls reconstruction and random matrix ensembles in compressed sensing"

Connected through hyperedge HE-2 (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-3 (induced by source paper "provable non convex optimization and algorithm validation via submodularity"):
  with members:
    - "continuous dr submodular maximization structure and algorithms"
    - "non monotone dr submodular function maximization"
    - "greedy maxcut algorithms and their information content"
    - "beyond convexity stochastic quasi convex optimization"
    - "scalable variational inference in log supermodular models"
    - "maximizing monotone submodular functions over the integer lattice"
    - "selecting the rank of truncated svd by maximum approximation capacity"
    - "submodular function maximization via the multilinear relaxation and contention resolution schemes"

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"
    - "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"

Connected through hyperedge HE-5 (induced by source paper "finite sample analysis of approximate message passing algorithms"):
  with members:
    - "analysis of approximate message passing with a class of non separable denoisers"
    - "rigorous dynamics of expectation propagation based signal recovery from unitarily invariant measurements"
    - "approximate message passing decoder and capacity achieving sparse superposition codes"
    - "capacity achieving sparse superposition codes via approximate message passing decoding"
    - "phase transitions and sample complexity in bayes optimal matrix factorization"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "mmse of probabilistic low rank matrix estimation universality with respect to the output channel"
    - "information theoretically optimal sparse pca"

Connected through hyperedge HE-6 (induced by source paper "exact guarantees on the absence of spurious local minima for non negative rank 1 robust principal component analysis"):
  with members:
    - "nonconvex optimization meets low rank matrix factorization an overview"
    - "nonconvex robust low rank matrix recovery"
    - "how much restricted isometry is needed in nonconvex matrix recovery"
    - "complete dictionary recovery over the sphere i overview and the geometric picture"
    - "global optimality in low rank matrix optimization"
    - "spectral algorithms for computing fair support vector machines"
    - "no spurious local minima in nonconvex low rank problems a unified geometric analysis"
    - "fast algorithms for robust pca via gradient descent"

Connected through hyperedge HE-7 (induced by source paper "continuous dr submodular maximization structure and algorithms"):
  with members:
    - "gradient methods for submodular maximization"
    - "robust budget allocation via continuous submodular functions"
    - "guaranteed non convex optimization submodular maximization over continuous domains"
    - "maximizing non monotone dr submodular functions with cardinality constraints"
    - "a reduction for optimizing lattice submodular functions with diminishing returns"
    - "constrained submodular maximization beyond 1 e"
    - "submodular functions from discrete to continous domains"
    - "submodular function maximization via the multilinear relaxation and contention resolution schemes"

Connected through hyperedge HE-8 (induced by source paper "multi processor approximate message passing using lossy compression"):
  with members:
    - "compressive imaging via approximate message passing with image denoising"
    - "bilinear generalized approximate message passing part i derivation"
    - "distributed compressed sensing for static and time varying networks"
    - "distributed sparse signal recovery for sensor networks"
    - "the dynamics of message passing on dense graphs with applications to compressed sensing"
    - "message passing algorithms for compressed sensing"

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)