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 "optimal bounds on approximation of submodular and xos functions by juntas"):
  Abstract: We investigate the approximability of several classes of real-valued functions by functions of a small number of variables ({\em juntas}). Our main results are tight bounds on the number of variables required to approximate a function $f:\{0,1\}^n \rightarrow [0,1]$ within $\ell_2$-error $\epsilon$ over the uniform distribution: 1. If $f$ is submodular, then it is $\epsilon$-close to a function of $O(\frac{1}{\epsilon^2} \log \frac{1}{\epsilon})$ variables. This is an exponential improvement over previously known results. We note that $\Omega(\frac{1}{\epsilon^2})$ variables are necessary even for linear functions. 2. If $f$ is fractionally subadditive (XOS) it is $\epsilon$-close to a function of $2^{O(1/\epsilon^2)}$ variables. This result holds for all functions with low total $\ell_1$-influence and is a real-valued analogue of Friedgut's theorem for boolean functions. We show that $2^{\Omega(1/\epsilon)}$ variables are necessary even for XOS functions. #R##N#As applications of these results, we provide learning algorithms over the uniform distribution. For XOS functions, we give a PAC learning algorithm that runs in time $2^{poly(1/\epsilon)} poly(n)$. For submodular functions we give an algorithm in the more demanding PMAC learning model (Balcan and Harvey, 2011) which requires a multiplicative $1+\gamma$ factor approximation with probability at least $1-\epsilon$ over the target distribution. Our uniform distribution algorithm runs in time $2^{poly(1/(\gamma\epsilon))} poly(n)$. This is the first algorithm in the PMAC model that over the uniform distribution can achieve a constant approximation factor arbitrarily close to 1 for all submodular functions. As follows from the lower bounds in (Feldman et al., 2013) both of these algorithms are close to optimal. We also give applications for proper learning, testing and agnostic learning with value queries of these classes.

Includes members:
  Member "representation approximation and learning of submodular functions using low rank decision trees":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")
  Member "learning coverage functions and private release of marginals":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")
  Member "dnf sparsification and a faster deterministic counting algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "analysis of boolean functions")
  Member "learning pseudo boolean k dnf and submodular functions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")
  Member "submodular functions are noise stable":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")
  Member "learning valuation functions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "powerset convolutional neural networks")
  Member "a note on concentration of submodular functions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "prophet inequalities with linear correlations and augmentations")
  Member "submodular functions learnability structure and optimization":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "subadditive load balancing")

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.DS(Data Structures and Algorithms)