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 optimal approximation factor in density estimation"):
  Abstract: Consider the following problem: given two arbitrary densities $q_1,q_2$ and a sample-access to an unknown target density $p$, find which of the $q_i$'s is closer to $p$ in total variation. #R##N#A remarkable result due to Yatracos shows that this problem is tractable in the following sense: there exists an algorithm that uses $O(\epsilon^{-2})$ samples from $p$ and outputs~$q_i$ such that with high probability, $TV(q_i,p) \leq 3\cdot\mathsf{opt} + \epsilon$, where $\mathsf{opt}= \min\{TV(q_1,p),TV(q_2,p)\}$. Moreover, this result extends to any finite class of densities $\mathcal{Q}$: there exists an algorithm that outputs the best density in $\mathcal{Q}$ up to a multiplicative approximation factor of 3. #R##N#We complement and extend this result by showing that: (i) the factor 3 can not be improved if one restricts the algorithm to output a density from $\mathcal{Q}$, and (ii) if one allows the algorithm to output arbitrary densities (e.g.\ a mixture of densities from $\mathcal{Q}$), then the approximation factor can be reduced to 2, which is optimal. In particular this demonstrates an advantage of improper learning over proper in this setup. #R##N#We develop two approaches to achieve the optimal approximation factor of 2: an adaptive one and a static one. Both approaches are based on a geometric point of view of the problem and rely on estimating surrogate metrics to the total variation. Our sample complexity bounds exploit techniques from {\it Adaptive Data Analysis}.

Includes members:
  Member "fast and sample near optimal algorithms for learning multidimensional histograms":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "monotone probability distributions over the boolean cube can be learned with sublinear samples")
  Member "list decodable robust mean estimation and learning mixtures of spherical gaussians":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "meta learning for mixed linear regression")
  Member "sample efficient learning of mixtures":
    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 "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 "algorithmic stability for adaptive data analysis":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "reasoning about generalization via conditional mutual information")
  Member "optimal learners for multiclass problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "generalization bounds in the predict then optimize framework")
  Member "near optimal density estimation in near linear time using variable width histograms":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "learning structured distributions from untrusted batches faster and simpler")
  Member "density estimation in linear time":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "locally private hypothesis selection")

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.LG(Machine Learning)