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: "sum of squares lower bounds for sparse pca"
  Abstract: This paper establishes a statistical versus computational trade-off for solving a basic high-dimensional machine learning problem via a basic convex relaxation method. Specifically, we consider the {\em Sparse Principal Component Analysis} (Sparse PCA) problem, and the family of {\em Sum-of-Squares} (SoS, aka Lasserre/Parillo) convex relaxations. It was well known that in large dimension $p$, a planted $k$-sparse unit vector can be {\em in principle} detected using only $n \approx k\log p$ (Gaussian or Bernoulli) samples, but all {\em efficient} (polynomial time) algorithms known require $n \approx k^2$ samples. It was also known that this quadratic gap cannot be improved by the the most basic {\em semi-definite} (SDP, aka spectral) relaxation, equivalent to a degree-2 SoS algorithms. Here we prove that also degree-4 SoS algorithms cannot improve this quadratic gap. This average-case lower bound adds to the small collection of hardness results in machine learning for this powerful family of convex relaxation algorithms. Moreover, our design of moments (or "pseudo-expectations") for this lower bound is quite different than previous lower bounds. Establishing lower bounds for higher degree SoS algorithms for remains a challenging problem.

Connected through hyperedge HE-1 (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"
    - "mutual information for symmetric rank one matrix estimation a proof of the replica formula"
    - "information theoretically optimal sparse pca"

Connected through hyperedge HE-2 (induced by source paper "the power of sum of squares for detecting hidden structures"):
  with members:
    - "exact tensor completion with sum of squares"
    - "a nearly tight sum of squares lower bound for the planted clique problem"
    - "polynomial time tensor decompositions with sum of squares"
    - "multiplicative approximations for polynomial optimization over the unit sphere"
    - "how well do local algorithms solve semidefinite programs"
    - "spectral algorithms for tensor completion"
    - "strongly refuting random csps below the spectral threshold"
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"

Connected through hyperedge HE-3 (induced by source paper "sparse phase retrieval via sparse pca despite model misspecification a simplified and extended analysis"):
  with members:
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"
    - "the generalized lasso with non linear observations"
    - "phase retrieval via wirtinger flow theory and algorithms"
    - "sparse phase retrieval convex algorithms and limitations"
    - "robust 1 bit compressed sensing and sparse logistic regression a convex programming approach"
    - "phaselift exact and stable signal recovery from magnitude measurements via convex programming"
    - "optimal solutions for sparse principal component analysis"

Connected through hyperedge HE-4 (induced by source paper "statistical query lower bounds for robust estimation of high dimensional gaussians and gaussian mixtures"):
  with members:
    - "being robust in high dimensions can be practical"
    - "robust sparse estimation tasks in high dimensions"
    - "robustly learning a gaussian getting optimal error efficiently"
    - "a size free clt for poisson multinomials and its applications"
    - "agnostic estimation of mean and covariance"
    - "robust estimators in high dimensions without the computational intractability"
    - "a general characterization of the statistical query complexity"
    - "beyond spectral tight bounds for planted gaussians"

Connected through hyperedge HE-5 (induced by source paper "finding a sparse vector in a subspace linear sparsity using alternating directions"):
  with members:
    - "a geometric analysis of phase retrieval"
    - "simple efficient and neural algorithms for sparse coding"
    - "solving random quadratic systems of equations is nearly as easy as solving linear systems"
    - "tensor vs matrix methods robust tensor decomposition under block sparse perturbations"
    - "speeding up sum of squares for tensor decomposition and planted sparse vectors"
    - "finding a low rank basis in a matrix subspace"
    - "dual principal component pursuit"
    - "complete dictionary recovery over the sphere"

Connected through hyperedge HE-6 (induced by source paper "a nearly tight sum of squares lower bound for the planted clique problem"):
  with members:
    - "improved sum of squares lower bounds for hidden clique and hidden submatrix problems"
    - "sum of squares lower bounds from pairwise independence"
    - "sos and planted clique tight analysis of mpw moments at all degrees and an optimal lower bound at degree four"
    - "sum of squares lower bounds for planted clique"
    - "dictionary learning and tensor decomposition via the sum of squares method"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "rounding sum of squares relaxations"
    - "hidden cliques and the certification of the restricted isometry property"

Connected through hyperedge HE-7 (induced by source paper "fast spectral algorithms from sum of squares proofs tensor decomposition and planted sparse vectors"):
  with members:
    - "finding a sparse vector in a subspace linear sparsity using alternating directions"
    - "a lasserre based 1 varepsilon approximation for pm mid p_j 1 textrm prec mid c_ max"
    - "learning mixtures of gaussians in high dimensions"
    - "decomposing overcomplete 3rd order tensors using sum of squares algorithms"
    - "tensor principal component analysis via sum of squares proofs"
    - "tensor prediction rademacher complexity and random 3 xor"
    - "powers of tensors and fast matrix multiplication"
    - "dictionary learning and tensor decomposition via the sum of squares method"

Connected through hyperedge HE-8 (induced by source paper "speeding up sum of squares for tensor decomposition and planted sparse vectors"):
  with members:
    - "finding a sparse vector in a subspace linear sparsity using alternating directions"
    - "learning mixtures of gaussians in high dimensions"
    - "decomposing overcomplete 3rd order tensors using sum of squares algorithms"
    - "tensor principal component analysis via sum of squares proofs"
    - "tensor prediction rademacher complexity and random 3 xor"
    - "a statistical model for tensor pca"
    - "sum of squares proofs and the quest toward optimal algorithms"
    - "a tensor approach to learning mixed membership community models"

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.LG(Machine Learning)