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 "optimal average case reductions to sparse pca from weak assumptions to strong hardness"):
  Abstract: In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the average-case complexity of sparse PCA through reductions from the planted clique (PC) conjecture - which conjectures that there is no polynomial-time algorithm to detect a planted clique of size $K = o(N^{1/2})$ in $\mathcal{G}(N, \frac{1}{2})$. All previous reductions to sparse PCA either fail to show tight computational lower bounds matching existing algorithms or show lower bounds for formulations of sparse PCA other than its canonical generative model, the spiked covariance model. Also, these lower bounds all quickly degrade with the exponent in the PC conjecture. Specifically, when only given the PC conjecture up to $K = o(N^\alpha)$ where $\alpha < 1/2$, there is no sparsity level $k$ at which these lower bounds remain tight. If $\alpha \le 1/3$ these reductions fail to even show the existence of a statistical-computational tradeoff at any sparsity $k$. We give a reduction from PC that yields the first full characterization of the computational barrier in the spiked covariance model, providing tight lower bounds at all sparsities $k$. We also show the surprising result that weaker forms of the PC conjecture up to clique size $K = o(N^\alpha)$ for any given $\alpha \in (0, 1/2]$ imply tight computational lower bounds for sparse PCA at sparsities $k = o(n^{\alpha/3})$. This shows that even a mild improvement in the signal strength needed by the best known polynomial-time sparse PCA algorithms would imply that the hardness threshold for PC is subpolynomial. This is the first instance of a suboptimal hardness assumption implying optimal lower bounds for another problem in unsupervised learning.

Includes members:
  Member "on finding dense common subgraphs":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "span core decomposition for temporal networks algorithms and applications")
  Member "reducibility and computational lower bounds for problems with planted sparse structure":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "adversarially robust low dimensional representations")
  Member "the power of sum of squares for detecting hidden structures":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "average case lower bounds for learning sparse mixtures robust estimation and semirandom adversaries")
  Member "statistical query lower bounds for robust estimation of high dimensional gaussians and gaussian mixtures":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "learning structured distributions from untrusted batches faster and simpler")
  Member "incoherence optimal matrix completion":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "matrix completion with prior subspace information via maximizing correlation")
  Member "label optimal regret bounds for online local learning":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "reducibility and computational lower bounds for problems with planted sparse structure")
  Member "random tensors and planted cliques":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "strongly refuting random csps below the spectral threshold")

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.CC(Computational Complexity)