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 "representation approximation and learning of submodular functions using low rank decision trees"):
  Abstract: We study the complexity of approximate representation and learning of submodular functions over the uniform distribution on the Boolean hypercube $\{0,1\}^n$. Our main result is the following structural theorem: any submodular function is $\epsilon$-close in $\ell_2$ to a real-valued decision tree (DT) of depth $O(1/\epsilon^2)$. This immediately implies that any submodular function is $\epsilon$-close to a function of at most $2^{O(1/\epsilon^2)}$ variables and has a spectral $\ell_1$ norm of $2^{O(1/\epsilon^2)}$. It also implies the closest previous result that states that submodular functions can be approximated by polynomials of degree $O(1/\epsilon^2)$ (Cheraghchi et al., 2012). Our result is proved by constructing an approximation of a submodular function by a DT of rank $4/\epsilon^2$ and a proof that any rank-$r$ DT can be $\epsilon$-approximated by a DT of depth $\frac{5}{2}(r+\log(1/\epsilon))$. #R##N#We show that these structural results can be exploited to give an attribute-efficient PAC learning algorithm for submodular functions running in time $\tilde{O}(n^2) \cdot 2^{O(1/\epsilon^{4})}$. The best previous algorithm for the problem requires $n^{O(1/\epsilon^{2})}$ time and examples (Cheraghchi et al., 2012) but works also in the agnostic setting. In addition, we give improved learning algorithms for a number of related settings. #R##N#We also prove that our PAC and agnostic learning algorithms are essentially optimal via two lower bounds: (1) an information-theoretic lower bound of $2^{\Omega(1/\epsilon^{2/3})}$ on the complexity of learning monotone submodular functions in any reasonable model; (2) computational lower bound of $n^{\Omega(1/\epsilon^{2/3})}$ based on a reduction to learning of sparse parities with noise, widely-believed to be intractable. These are the first lower bounds for learning of submodular functions over the uniform distribution.

Includes members:
  Member "learning pseudo boolean k dnf and submodular functions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (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-2 (induced by source paper "approximate mathbb f _2 sketching of valuation functions")
  Member "private data release via learning thresholds":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "the power of factorization mechanisms in local and central differential privacy")
  Member "learning valuation functions":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "powerset convolutional neural networks")
  Member "from convex optimization to randomized mechanisms toward optimal combinatorial auctions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "improved truthful mechanisms for combinatorial auctions with submodular bidders")
  Member "a note on concentration of submodular functions":
    also connected through other hyperedges:
      - Hyperedge HE-6 (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-7 (induced by source paper "subadditive load balancing")
  Member "a complete characterization of statistical query learning with applications to evolvability":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "computational complexity analysis of genetic programming")

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)