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 "an improved analysis of the er spud dictionary learning algorithm"):
  Abstract: In "dictionary learning" we observe $Y = AX + E$ for some $Y\in\mathbb{R}^{n\times p}$, $A \in\mathbb{R}^{m\times n}$, and $X\in\mathbb{R}^{m\times p}$. The matrix $Y$ is observed, and $A, X, E$ are unknown. Here $E$ is "noise" of small norm, and $X$ is column-wise sparse. The matrix $A$ is referred to as a {\em dictionary}, and its columns as {\em atoms}. Then, given some small number $p$ of samples, i.e.\ columns of $Y$, the goal is to learn the dictionary $A$ up to small error, as well as $X$. The motivation is that in many applications data is expected to sparse when represented by atoms in the "right" dictionary $A$ (e.g.\ images in the Haar wavelet basis), and the goal is to learn $A$ from the data to then use it for other applications. #R##N#Recently, [SWW12] proposed the dictionary learning algorithm ER-SpUD with provable guarantees when $E = 0$ and $m = n$. They showed if $X$ has independent entries with an expected $s$ non-zeroes per column for $1 \lesssim s \lesssim \sqrt{n}$, and with non-zero entries being subgaussian, then for $p\gtrsim n^2\log^2 n$ with high probability ER-SpUD outputs matrices $A', X'$ which equal $A, X$ up to permuting and scaling columns (resp.\ rows) of $A$ (resp.\ $X$). They conjectured $p\gtrsim n\log n$ suffices, which they showed was information theoretically necessary for {\em any} algorithm to succeed when $s \simeq 1$. Significant progress was later obtained in [LV15]. #R##N#We show that for a slight variant of ER-SpUD, $p\gtrsim n\log(n/\delta)$ samples suffice for successful recovery with probability $1-\delta$. We also show that for the unmodified ER-SpUD, $p\gtrsim n^{1.99}$ samples are required even to learn $A, X$ with polynomially small success probability. This resolves the main conjecture of [SWW12], and contradicts the main result of [LV15], which claimed that $p\gtrsim n\log^4 n$ guarantees success whp.

Includes members:
  Member "complete dictionary recovery over the sphere":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "more algorithms for provable dictionary learning":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "the non convex geometry of low rank matrix optimization")
  Member "max vs min tensor decomposition and ica with nearly linear sample complexity":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "agnostic estimation of mean and covariance")
  Member "sparse modeling for image and vision processing":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "dictionary learning and tensor decomposition via the sum of squares method":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "new algorithms for learning incoherent and overcomplete dictionaries":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "when can wasserstein gans minimize wasserstein distance")
  Member "fourier pca and robust tensor decomposition":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "learning two layer rectified neural networks in polynomial time")
  Member "blind signal separation in the presence of gaussian noise":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "geometric methods for robust data analysis in high dimension")

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)