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 "empirical risk minimization for stochastic convex optimization o 1 n and o 1 n 2 type of risk bounds"):
  Abstract: Although there exist plentiful theories of empirical risk minimization (ERM) for supervised learning, current theoretical understandings of ERM for a related problem---stochastic convex optimization (SCO), are limited. In this work, we strengthen the realm of ERM for SCO by exploiting smoothness and strong convexity conditions to improve the risk bounds. First, we establish an $\widetilde{O}(d/n + \sqrt{F_*/n})$ risk bound when the random function is nonnegative, convex and smooth, and the expected function is Lipschitz continuous, where $d$ is the dimensionality of the problem, $n$ is the number of samples, and $F_*$ is the minimal risk. Thus, when $F_*$ is small we obtain an $\widetilde{O}(d/n)$ risk bound, which is analogous to the $\widetilde{O}(1/n)$ optimistic rate of ERM for supervised learning. Second, if the objective function is also $\lambda$-strongly convex, we prove an $\widetilde{O}(d/n + \kappa F_*/n )$ risk bound where $\kappa$ is the condition number, and improve it to $O(1/[\lambda n^2] + \kappa F_*/n)$ when $n=\widetilde{\Omega}(\kappa d)$. As a result, we obtain an $O(\kappa/n^2)$ risk bound under the condition that $n$ is large and $F_*$ is small, which to the best of our knowledge, is the first $O(1/n^2)$-type of risk bound of ERM. Third, we stress that the above results are established in a unified framework, which allows us to derive new risk bounds under weaker conditions, e.g., without convexity of the random function and Lipschitz continuity of the expected function. Finally, we demonstrate that to achieve an $O(1/[\lambda n^2] + \kappa F_*/n)$ risk bound for supervised learning, the $\widetilde{\Omega}(\kappa d)$ requirement on $n$ can be replaced with $\Omega(\kappa^2)$, which is dimensionality-independent.

Includes members:
  Member "from exp concavity to variance control high probability o 1 n rates and high probability online to batch conversion":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient improper learning for online logistic regression")
  Member "average stability is invariant to data preconditioning implications to exp concave empirical risk minimization":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "an exact no free lunch theorem for community detection")
  Member "generalization of erm in stochastic convex optimization the dimension strikes back":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "reasoning about generalization via conditional mutual information")
  Member "making gradient descent optimal for strongly convex stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "wireless federated learning with local differential privacy")
  Member "optimistic rates for learning with a smooth loss":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "theoretical analysis of divide and conquer erm beyond square loss and rkhs")

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)