human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "the power of sum of squares for detecting hidden structures"):
  Abstract: We study planted problems---finding hidden structures in random noisy inputs---through the lens of the sum-of-squares semidefinite programming hierarchy (SoS). This family of powerful semidefinite programs has recently yielded many new algorithms for planted problems, often achieving the best known polynomial-time guarantees in terms of accuracy of recovered solutions and robustness to noise. One theme in recent work is the design of spectral algorithms which match the guarantees of SoS algorithms for planted problems. Classical spectral algorithms are often unable to accomplish this: the twist in these new spectral algorithms is the use of spectral structure of matrices whose entries are low-degree polynomials of the input variables. We prove that for a wide class of planted problems, including refuting random constraint satisfaction problems, tensor and sparse PCA, densest-k-subgraph, community detection in stochastic block models, planted clique, and others, eigenvalues of degree-d matrix polynomials are as powerful as SoS semidefinite programs of roughly degree d. For such problems it is therefore always possible to match the guarantees of SoS without solving a large semidefinite program. Using related ideas on SoS algorithms and low-degree matrix polynomials (and inspired by recent work on SoS and the planted clique problem by Barak et al.), we prove new nearly-tight SoS lower bounds for the tensor and sparse principal component analysis problems. Our lower bounds for sparse principal component analysis are the first to suggest that going beyond existing algorithms for this problem may require sub-exponential time.

Includes members:
  Member "exact tensor completion with sum of squares":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "nonconvex low rank symmetric tensor completion from noisy data")
  Member "a nearly tight sum of squares lower bound for the planted clique problem":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")
  Member "polynomial time tensor decompositions with sum of squares":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "efficiently learning structured distributions from untrusted batches")
  Member "multiplicative approximations for polynomial optimization over the unit sphere":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the kikuchi hierarchy and tensor pca")
  Member "how well do local algorithms solve semidefinite programs":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "vector colorings of random ramanujan and large girth irregular graphs")
  Member "spectral algorithms for tensor completion":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "nonconvex low rank symmetric tensor completion from noisy data")
  Member "strongly refuting random csps below the spectral threshold":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "improved sum of squares lower bounds for hidden clique and hidden submatrix problems":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "broadcast congested clique planted cliques and pseudorandom generators")

Question: Please tell me which class the source paper 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.DS(Data Structures and Algorithms)