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 "on learning mixtures of well separated gaussians"):
  Abstract: We consider the problem of efficiently learning mixtures of a large number of spherical Gaussians, when the components of the mixture are well separated. In the most basic form of this problem, we are given samples from a uniform mixture of $k$ standard spherical Gaussians, and the goal is to estimate the means up to accuracy $\delta$ using $poly(k,d, 1/\delta)$ samples. #R##N#In this work, we study the following question: what is the minimum separation needed between the means for solving this task? The best known algorithm due to Vempala and Wang [JCSS 2004] requires a separation of roughly $\min\{k,d\}^{1/4}$. On the other hand, Moitra and Valiant [FOCS 2010] showed that with separation $o(1)$, exponentially many samples are required. We address the significant gap between these two bounds, by showing the following results. #R##N#1. We show that with separation $o(\sqrt{\log k})$, super-polynomially many samples are required. In fact, this holds even when the $k$ means of the Gaussians are picked at random in $d=O(\log k)$ dimensions. #R##N#2. We show that with separation $\Omega(\sqrt{\log k})$, $poly(k,d,1/\delta)$ samples suffice. Note that the bound on the separation is independent of $\delta$. This result is based on a new and efficient "accuracy boosting" algorithm that takes as input coarse estimates of the true means and in time $poly(k,d, 1/\delta)$ outputs estimates of the means up to arbitrary accuracy $\delta$ assuming the separation between the means is $\Omega(\min\{\sqrt{\log k},\sqrt{d}\})$ (independently of $\delta$). #R##N#We also present a computationally efficient algorithm in $d=O(1)$ dimensions with only $\Omega(\sqrt{d})$ separation. These results together essentially characterize the optimal order of separation between components that is needed to learn a mixture of $k$ spherical Gaussians with polynomial samples.

Includes members:
  Member "statistical query lower bounds for robust estimation of high dimensional gaussians and gaussian mixtures":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "learning structured distributions from untrusted batches faster and simpler")
  Member "learning mixtures of gaussians in high dimensions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "monotone probability distributions over the boolean cube can be learned with sublinear samples")
  Member "tight bounds for learning a mixture of two gaussians":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "em algorithm is sample optimal for learning mixtures of well separated gaussians")
  Member "smoothed analysis of tensor decompositions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "improper learning for non stochastic control")
  Member "uniqueness of tensor decompositions with applications to polynomial identifiability":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "smoothed analysis in unsupervised learning via decoupling")
  Member "faster and sample near optimal algorithms for proper learning mixtures of gaussians":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "locally private hypothesis selection")
  Member "the more the merrier the blessing of dimensionality for learning large gaussian mixtures":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "em algorithm is sample optimal for learning mixtures of well separated gaussians")
  Member "fourier pca and robust tensor decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "learning two layer rectified neural networks in polynomial time")

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)