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 "message passing for maximum weight independent set"):
  Abstract: In this paper, we investigate the use of message-passing algorithms for the problem of finding the max-weight independent set (MWIS) in a graph. First, we study the performance of the classical loopy max-product belief propagation. We show that each fixed-point estimate of max product can be mapped in a natural way to an extreme point of the linear programming (LP) polytope associated with the MWIS problem. However, this extreme point may not be the one that maximizes the value of node weights; the particular extreme point at final convergence depends on the initialization of max product. We then show that if max product is started from the natural initialization of uninformative messages, it always solves the correct LP, if it converges. This result is obtained via a direct analysis of the iterative algorithm, and cannot be obtained by looking only at fixed points. The tightness of the LP relaxation is thus necessary for max-product optimality, but it is not sufficient. Motivated by this observation, we show that a simple modification of max product becomes gradient descent on (a smoothed version of) the dual of the LP, and converges to the dual optimum. We also develop a message-passing algorithm that recovers the primal MWIS solution from the output of the descent algorithm. We show that the MWIS estimate obtained using these two algorithms in conjunction is correct when the graph is bipartite and the MWIS is unique. Finally, we show that any problem of maximum a posteriori (MAP) estimation for probability distributions over finite domains can be reduced to an MWIS problem. We believe this reduction will yield new insights and algorithms for MAP estimation.

Includes members:
  Member "map estimation linear programming and belief propagation with convex free energies":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")
  Member "on the optimality of tree reweighted max product message passing":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "partial optimality of dual decomposition for map inference in pairwise mrfs")
  Member "belief propagation for weighted b matchings on arbitrary graphs and its relation to linear programs with integer solutions":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "pils exploring high order neighborhoods by pattern mining and injection")
  Member "max product for maximum weight matching convergence correctness and lp duality":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "my fair bandit distributed learning of max min fairness with multi player bandits")
  Member "convergence of min sum message passing for quadratic optimization":
    also connected through other hyperedges:
      (none)
  Member "convergence of the min sum message passing algorithm for quadratic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "message passing algorithms reparameterizations and splittings")

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.AI(Artificial Intelligence)