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 kikuchi hierarchy and tensor pca"):
  Abstract: For the tensor PCA (principal component analysis) problem, we propose a new hierarchy of algorithms that are increasingly powerful yet require increasing runtime. Our hierarchy is analogous to the sum-of-squares (SOS) hierarchy but is instead inspired by statistical physics and related algorithms such as belief propagation and AMP (approximate message passing). Our level-$\ell$ algorithm can be thought of as a (linearized) message-passing algorithm that keeps track of $\ell$-wise dependencies among the hidden variables. Specifically, our algorithms are spectral methods based on the Kikuchi Hessian matrix, which generalizes the well-studied Bethe Hessian matrix to the higher-order Kikuchi free energies. #R##N#It is known that AMP, the flagship algorithm of statistical physics, has substantially worse performance than SOS for tensor PCA. In this work we `redeem' the statistical physics approach by showing that our hierarchy gives a polynomial-time algorithm matching the performance of SOS. Our hierarchy also yields a continuum of subexponential-time algorithms, and we prove that these achieve the same (conjecturally optimal) tradeoff between runtime and statistical power as SOS. Our results hold for even-order tensors, and we conjecture that they also hold for odd-order tensors. #R##N#Our methods suggest a new avenue for systematically obtaining optimal algorithms for Bayesian inference problems, and our results constitute a step toward unifying the statistical physics and sum-of-squares approaches to algorithm design.

Includes members:
  Member "the power of sum of squares for detecting hidden structures":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "average case lower bounds for learning sparse mixtures robust estimation and semirandom adversaries")
  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 "sum of squares certificates for maxima of random tensors on the sphere":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "weak decoupling polynomial folds and approximate optimization over the sphere")
  Member "multiplicative approximations for polynomial optimization over the unit sphere":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "the power of sum of squares for detecting hidden structures")
  Member "mutual information for symmetric rank one matrix estimation a proof of the replica formula":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "capacity achieving spatially coupled sparse superposition codes with amp decoding")
  Member "strongly refuting random csps below the spectral threshold":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")
  Member "phase transitions in sparse pca":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "the error probability of sparse superposition codes with approximate message passing decoding")
  Member "how to refute a random csp":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "time space tradeoffs for distinguishing distributions and applications to security of goldreich s prg")

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)