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 "subdeterminant maximization via nonconvex relaxations and anti concentration"):
  Abstract: Several fundamental problems that arise in optimization and computer science can be cast as follows: Given vectors $v_1,\ldots,v_m \in \mathbb{R}^d$ and a constraint family ${\cal B}\subseteq 2^{[m]}$, find a set $S \in \cal{B}$ that maximizes the squared volume of the simplex spanned by the vectors in $S$. A motivating example is the data-summarization problem in machine learning where one is given a collection of vectors that represent data such as documents or images. The volume of a set of vectors is used as a measure of their diversity, and partition or matroid constraints over $[m]$ are imposed in order to ensure resource or fairness constraints. Recently, Nikolov and Singh presented a convex program and showed how it can be used to estimate the value of the most diverse set when ${\cal B}$ corresponds to a partition matroid. This result was recently extended to regular matroids in works of Straszak and Vishnoi, and Anari and Oveis Gharan. The question of whether these estimation algorithms can be converted into the more useful approximation algorithms -- that also output a set -- remained open. #R##N#The main contribution of this paper is to give the first approximation algorithms for both partition and regular matroids. We present novel formulations for the subdeterminant maximization problem for these matroids; this reduces them to the problem of finding a point that maximizes the absolute value of a nonconvex function over a Cartesian product of probability simplices. The technical core of our results is a new anti-concentration inequality for dependent random variables that allows us to relate the optimal value of these nonconvex functions to their value at a random point. Unlike prior work on the constrained subdeterminant maximization problem, our proofs do not rely on real-stability or convexity and could be of independent interest both in algorithms and complexity.

Includes members:
  Member "a generalization of permanent inequalities and applications in counting and optimization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "how to be fair and diverse":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "representation learning with statistical independence to mitigate bias")
  Member "on the complexity of constrained determinantal point processes":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "fair and diverse dpp based data summarization")
  Member "real stable polynomials and matroids optimization and counting":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "dynamic sampling from graphical models")
  Member "analysis of boolean functions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "coarse grained complexity for dynamic algorithms")
  Member "on largest volume simplices and sub determinants":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "maximizing the number of spanning trees in a connected graph")
  Member "randomized rounding for the largest simplex problem":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "batch active learning using determinantal point processes")
  Member "a robust khintchine inequality and algorithms for computing optimal constants in fourier analysis and high dimensional geometry":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "on the complexity of the inverse semivalue problem for weighted voting games")

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)