human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "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.

Connected through hyperedge HE-1 (induced by source paper "theoretical analysis of divide and conquer erm beyond square loss and rkhs"):
  with members:
    - "divide and conquer local average regression"
    - "distributed learning with regularized least squares"
    - "refined error bounds for several learning algorithms"
    - "distributed autonomous online learning regrets and intrinsic privacy preserving properties"
    - "optimistic rates for learning with a smooth loss"

Connected through hyperedge HE-2 (induced by source paper "solving empirical risk minimization in the current matrix multiplication time"):
  with members:
    - "nearly sample optimal sparse fourier transform in any dimension ripless and filterless"
    - "limits on all known and some unknown approaches to matrix multiplication"
    - "solving linear programs in the current matrix multiplication time"
    - "on the local minima of the empirical risk"
    - "limits on the universal method for matrix multiplication"
    - "guaranteed sufficient decrease for variance reduced stochastic gradient descent"
    - "variance reduced stochastic gradient descent with sufficient decrease"
    - "improved rectangular matrix multiplication using powers of the coppersmith winograd tensor"

Connected through hyperedge HE-3 (induced by source paper "stochastic approximation of smooth and strongly convex functions beyond the o 1 t convergence rate"):
  with members:
    - "a hitting time analysis of stochastic gradient langevin dynamics"
    - "memory and communication efficient distributed stochastic optimization with minibatch prox"
    - "from exp concavity to variance control high probability o 1 n rates and high probability online to batch conversion"
    - "generalization of erm in stochastic convex optimization the dimension strikes back"
    - "escaping from saddle points online stochastic gradient for tensor decomposition"
    - "passive learning with target risk"
    - "stochastic gradient descent for non smooth optimization convergence results and optimal averaging schemes"
    - "making gradient descent optimal for strongly convex stochastic optimization"

Connected through hyperedge HE-4 (induced by source paper "learning with non convex truncated losses by sgd"):
  with members:
    - "fast rates for general unbounded loss functions from erm to generalized bayes"
    - "learning without concentration"
    - "from stochastic mixability to fast rates"
    - "relative deviation learning bounds and generalization with unbounded loss functions"
    - "loss minimization and parameter estimation with heavy tails"

Connected through hyperedge HE-5 (induced by source paper "max diversity distributed learning theory and algorithms"):
  with members:
    - "distributed learning with regularized least squares"
    - "optimistic rates for learning with a smooth loss"

Question: Please tell me which class the center node 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)