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 the regret minimization of nonconvex online gradient ascent for online pca"):
  Abstract: In this paper we focus on the problem of Online Principal Component Analysis in the regret minimization framework. For this problem, all existing regret minimization algorithms for the fully-adversarial setting are based on a positive semidefinite convex relaxation, and hence require quadratic memory and SVD computation (either thin of full) on each iteration, which amounts to at least quadratic runtime per iteration. This is in stark contrast to a corresponding stochastic i.i.d. variant of the problem, which was studied extensively lately, and admits very efficient gradient ascent algorithms that work directly on the natural non-convex formulation of the problem, and hence require only linear memory and linear runtime per iteration. This raises the question: can non-convex online gradient ascent algorithms be shown to minimize regret in online adversarial settings? In this paper we take a step forward towards answering this question. We introduce an \textit{adversarially-perturbed spiked-covariance model} in which, each data point is assumed to follow a fixed stochastic distribution with a non-zero spectral gap in the covariance matrix, but is then perturbed with some adversarial vector. This model is a natural extension of a well studied standard stochastic setting that allows for non-stationary (adversarial) patterns to arise in the data and hence, might serve as a significantly better approximation for real-world data-streams. We show that in an interesting regime of parameters, when the non-convex online gradient ascent algorithm is initialized with a "warm-start" vector, it provably minimizes the regret with high probability. We further discuss the possibility of computing such a "warm-start" vector, and also the use of regularization to obtain fast regret rates. Our theoretical findings are supported by empirical experiments on both synthetic and real-world data.

Includes members:
  Member "introduction to online convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "beyond ucb optimal and efficient contextual bandits with regression oracles")
  Member "follow the compressed leader faster online learning of eigenvectors and faster mmwu":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "distributed stochastic algorithms for high rate streaming principal component analysis")
  Member "streaming pca matching matrix bernstein and near optimal finite sample guarantees for oja s algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "distributed stochastic algorithms for high rate streaming principal component analysis")
  Member "matrix completion has no spurious local minimum":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "finding the sparsest vectors in a subspace theory algorithms and applications")
  Member "provable efficient online matrix completion via non convex stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "understanding the downstream instability of word embeddings")
  Member "convergence of stochastic gradient descent for pca":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "exponentially convergent stochastic k pca without variance reduction")
  Member "the fast convergence of incremental pca":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "distributed stochastic algorithms for high rate streaming principal component analysis")
  Member "provable bounds for learning some deep representations":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "span recovery for deep neural networks with applications to input obfuscation")

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)