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 "generalization of erm in stochastic convex optimization the dimension strikes back"):
  Abstract: In stochastic convex optimization the goal is to minimize a convex function $F(x) \doteq {\mathbf E}_{{\mathbf f}\sim D}[{\mathbf f}(x)]$ over a convex set $\cal K \subset {\mathbb R}^d$ where $D$ is some unknown distribution and each $f(\cdot)$ in the support of $D$ is convex over $\cal K$. The optimization is commonly based on i.i.d.~samples $f^1,f^2,\ldots,f^n$ from $D$. A standard approach to such problems is empirical risk minimization (ERM) that optimizes $F_S(x) \doteq \frac{1}{n}\sum_{i\leq n} f^i(x)$. Here we consider the question of how many samples are necessary for ERM to succeed and the closely related question of uniform convergence of $F_S$ to $F$ over $\cal K$. We demonstrate that in the standard $\ell_p/\ell_q$ setting of Lipschitz-bounded functions over a $\cal K$ of bounded radius, ERM requires sample size that scales linearly with the dimension $d$. This nearly matches standard upper bounds and improves on $\Omega(\log d)$ dependence proved for $\ell_2/\ell_2$ setting by Shalev-Shwartz et al. (2009). In stark contrast, these problems can be solved using dimension-independent number of samples for $\ell_2/\ell_2$ setting and $\log d$ dependence for $\ell_1/\ell_\infty$ setting using other approaches. We further show that our lower bound applies even if the functions in the support of $D$ are smooth and efficiently computable and even if an $\ell_1$ regularization term is added. Finally, we demonstrate that for a more general class of bounded-range (but not Lipschitz-bounded) stochastic convex programs an infinite gap appears already in dimension 2.

Includes members:
  Member "escaping the local minima via simulated annealing optimization of approximately convex functions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "simulated tempering langevin monte carlo ii an improved proof using soft markov chain decomposition")
  Member "statistical query algorithms for mean vector estimation and stochastic convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "limits on gradient compression for stochastic optimization")
  Member "generalization in adaptive data analysis and holdout reuse":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reasoning about generalization via conditional mutual information")
  Member "train faster generalize better stability of stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "disentangling adaptive gradient methods from learning rates")
  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 "sequential probability assignment with binary alphabets and large classes of experts":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "logistic regression the importance of being improper")
  Member "preserving statistical validity in adaptive data analysis":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "reasoning about generalization via conditional mutual information")
  Member "non strongly convex smooth stochastic approximation with convergence rate o 1 n":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "efficient and robust algorithms for adversarial linear contextual bandits")

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)