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 "norm product belief propagation primal dual message passing for approximate inference"):
  Abstract: In this paper we treat both forms of probabilistic inference, estimating marginal probabilities of the joint distribution and finding the most probable assignment, through a unified message-passing algorithm architecture. We generalize the Belief Propagation (BP) algorithms of sum-product and max-product and tree-rewaighted (TRW) sum and max product algorithms (TRBP) and introduce a new set of convergent algorithms based on "convex-free-energy" and Linear-Programming (LP) relaxation as a zero-temprature of a convex-free-energy. The main idea of this work arises from taking a general perspective on the existing BP and TRBP algorithms while observing that they all are reductions from the basic optimization formula of $f + \sum_i h_i$ where the function $f$ is an extended-valued, strictly convex but non-smooth and the functions $h_i$ are extended-valued functions (not necessarily convex). We use tools from convex duality to present the "primal-dual ascent" algorithm which is an extension of the Bregman successive projection scheme and is designed to handle optimization of the general type $f + \sum_i h_i$. Mapping the fractional-free-energy variational principle to this framework introduces the "norm-product" message-passing. Special cases include sum-product and max-product (BP algorithms) and the TRBP algorithms. When the fractional-free-energy is set to be convex (convex-free-energy) the norm-product is globally convergent for estimating of marginal probabilities and for approximating the LP-relaxation. We also introduce another branch of the norm-product, the "convex-max-product". The convex-max-product is convergent (unlike max-product) and aims at solving the LP-relaxation.

Includes members:
  Member "sufficient conditions for convergence of loopy belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient attack graph analysis through approximate inference")
  Member "convergent message passing algorithms for inference over general graphs with convex free energies":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")
  Member "map estimation linear programming and belief propagation with convex free energies":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")
  Member "convergent message passing algorithms a unifying view":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "graph structured prediction energy networks")
  Member "tightening lp relaxations for map using message passing":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "graph structured prediction energy networks")
  Member "on the optimality of tree reweighted max product message passing":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "partial optimality of dual decomposition for map inference in pairwise mrfs")
  Member "convexifying the bethe free energy":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference")
  Member "convergent propagation algorithms via oriented trees":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "lifted tree reweighted variational inference")

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)