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: "private empirical risk minimization beyond the worst case the effect of the constraint set geometry"
  Abstract: Empirical Risk Minimization (ERM) is a standard technique in machine learning, where a model is selected by minimizing a loss function over constraint set. When the training dataset consists of private information, it is natural to use a differentially private ERM algorithm, and this problem has been the subject of a long line of work started with Chaudhuri and Monteleoni 2008. A private ERM algorithm outputs an approximate minimizer of the loss function and its error can be measured as the difference from the optimal value of the loss function. When the constraint set is arbitrary, the required error bounds are fairly well understood~\cite{BassilyST14}. In this work, we show that the geometric properties of the constraint set can be used to derive significantly better results. Specifically, we show that a differentially private version of Mirror Descent leads to error bounds of the form $\tilde{O}(G_{\mathcal{C}}/n)$ for a lipschitz loss function, improving on the $\tilde{O}(\sqrt{p}/n)$ bounds in Bassily, Smith and Thakurta 2014. Here $p$ is the dimensionality of the problem, $n$ is the number of data points in the training set, and $G_{\mathcal{C}}$ denotes the Gaussian width of the constraint set that we optimize over. We show similar improvements for strongly convex functions, and for smooth functions. In addition, we show that when the loss function is Lipschitz with respect to the $\ell_1$ norm and $\mathcal{C}$ is $\ell_1$-bounded, a differentially private version of the Frank-Wolfe algorithm gives error bounds of the form $\tilde{O}(n^{-2/3})$. This captures the important and common case of sparse linear regression (LASSO), when the data $x_i$ satisfies $|x_i|_{\infty} \leq 1$ and we optimize over the $\ell_1$ ball. We show new lower bounds for this setting, that together with known bounds, imply that all our upper bounds are tight.

Connected through hyperedge HE-1 (induced by source paper "privately learning markov random fields"):
  with members:
    - "lower bounds for testing graphical models colorings and antiferromagnetic ising models"
    - "private hypothesis selection"
    - "data dependent differentially private parameter learning for directed graphical models"
    - "graphical model based estimation and inference for differential privacy"
    - "privately learning high dimensional distributions"
    - "sparse logistic regression learns all discrete pairwise graphical models"
    - "inspectre privately estimating the unseen"
    - "learning graphical models using multiplicative weights"

Connected through hyperedge HE-2 (induced by source paper "evaluating differentially private machine learning in practice"):
  with members:
    - "differentially private model publishing for deep learning"
    - "privacy preserving collaborative deep learning with irregular participants"
    - "cache telepathy leveraging shared resource attacks to learn dnn architectures"
    - "differentially private empirical risk minimization revisited faster and more general"
    - "dp admm admm based distributed learning with differential privacy"
    - "how to backdoor federated learning"
    - "ml leaks model and data independent membership inference attacks and defenses on machine learning models"
    - "efficient deep learning on multi source private data"

Connected through hyperedge HE-3 (induced by source paper "the cost of a reductions approach to private fair optimization"):
  with members:
    - "unleashing linear optimizers for group fair learning and optimization"
    - "differentially private empirical risk minimization revisited faster and more general"
    - "privacy amplification by iteration"
    - "a reductions approach to fair classification"
    - "multi objective bandits optimizing the generalized gini index"
    - "equality of opportunity in supervised learning"
    - "concentrated differential privacy simplifications extensions and lower bounds"
    - "concentrated differential privacy"

Connected through hyperedge HE-4 (induced by source paper "differentially private empirical risk minimization with sparsity inducing norms"):
  with members:
    - "differentially private empirical risk minimization revisited faster and more general"
    - "efficient private erm for smooth objectives"
    - "bolt on differential privacy for scalable stochastic gradient descent based analytics"
    - "calibrating data to sensitivity in private data analysis"
    - "learning with submodular functions a convex optimization perspective"
    - "structured sparsity inducing norms through submodular functions"
    - "differentially private empirical risk minimization"

Connected through hyperedge HE-5 (induced by source paper "differentially private empirical risk minimization revisited faster and more general"):
  with members:
    - "private incremental regression"
    - "the price of differential privacy for online learning"
    - "beyond convexity stochastic quasi convex optimization"
    - "revisiting differentially private regression lessons from learning theory and their consequences"
    - "improved svrg for non strongly convex or sum of non convex objectives"
    - "calibrating data to sensitivity in private data analysis"
    - "differentially private online learning"
    - "differentially private empirical risk minimization"

Connected through hyperedge HE-6 (induced by source paper "private incremental regression"):
  with members:
    - "private matchings and allocations"
    - "private approximations of the 2nd moment matrix using existing techniques in linear regression"
    - "sketching as a tool for numerical linear algebra"
    - "randomness efficient fast johnson lindenstrauss transform with applications in differential privacy and compressed sensing"
    - "differentially private empirical risk minimization efficient algorithms and tight error bounds"
    - "circulant matrices and differential privacy"
    - "private multiplicative weights beyond linear queries"
    - "privacy via the johnson lindenstrauss transform"

Connected through hyperedge HE-7 (induced by source paper "efficient private erm for smooth objectives"):
  with members:
    - "train faster generalize better stability of stochastic gradient descent"
    - "calibrating data to sensitivity in private data analysis"
    - "differentially private empirical risk minimization"
    - "learning in a large function space privacy preserving mechanisms for svm learning"

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)