human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "map estimation linear programming and belief propagation with convex free energies"
  Abstract: Finding the most probable assignment (MAP) in a general graphical model is known to be NP hard but good approximations have been attained with max-product belief propagation (BP) and its variants. In particular, it is known that using BP on a single-cycle graph or tree reweighted BP on an arbitrary graph will give the MAP solution if the beliefs have no ties. In this paper we extend the setting under which BP can be used to provably extract the MAP. We define Convex BP as BP algorithms based on a convex free energy approximation and show that this class includes ordinary BP with single-cycle, tree reweighted BP and many other BP variants. We show that when there are no ties, fixed-points of convex max-product BP will provably give the MAP solution. We also show that convex sum-product BP at sufficiently small temperatures can be used to solve linear programs that arise from relaxing the MAP problem. Finally, we derive a novel condition that allows us to derive the MAP solution even if some of the convex BP beliefs have ties. In experiments, we show that our theorems allow us to find the MAP in many real-world instances of graphical models where exact inference using junction-tree is impossible.

Connected through hyperedge HE-1 (induced by source paper "convergence rates of smooth message passing with rounding in entropy regularized map inference"):
  with members:
    - "near linear time approximation algorithms for optimal transport via sinkhorn iteration"
    - "convergent message passing algorithms for inference over general graphs with convex free energies"
    - "convexifying the bethe free energy"

Connected through hyperedge HE-2 (induced by source paper "graph structured prediction energy networks"):
  with members:
    - "deep structured prediction with nonlinear output transformations"
    - "learning approximate inference networks for structured prediction"
    - "deep value networks learn to evaluate and iteratively refine structured outputs"
    - "end to end sequence labeling via bi directional lstm cnns crf"
    - "neural architectures for named entity recognition"
    - "structured prediction energy networks"
    - "deeply learning the messages in message passing inference"
    - "conditional random fields as recurrent neural networks"

Connected through hyperedge HE-3 (induced by source paper "iterative receivers for downlink mimo scma message passing and distributed cooperative detection"):
  with members:
    - "wireless powered communications with non orthogonal multiple access"
    - "nonorthogonal multiple access in large scale underlay cognitive radio networks"
    - "a survey of downlink non orthogonal multiple access for 5g wireless communication networks"
    - "gaussian message passing iterative detection for mimo noma systems with massive access"
    - "fast admm algorithm for distributed optimization with adaptive penalty"
    - "scma codebook design"
    - "what will 5g be"
    - "on the performance of non orthogonal multiple access in 5g systems with randomly deployed users"

Connected through hyperedge HE-4 (induced by source paper "high dimensional inference with random maximum a posteriori perturbations"):
  with members:
    - "direct optimization through arg max for discrete variational auto encoder"
    - "approximate inference via weighted rademacher complexity"
    - "the concrete distribution a continuous relaxation of discrete random variables"
    - "taming the curse of dimensionality discrete integration by hashing and optimization"
    - "on measure concentration of random maximum a posteriori perturbations"
    - "optimization with parity constraints from binary codes to discrete integration"
    - "on sampling from the gibbs distribution with random maximum a posteriori perturbations"
    - "on the partition function and random maximum a posteriori perturbations"

Connected through hyperedge HE-5 (induced by source paper "message passing and combinatorial optimization"):
  with members:
    - "augmentative message passing for traveling salesman problem and graph partitioning"
    - "perturbed message passing for constraint satisfaction problems"
    - "revisiting algebra and complexity of inference in graphical models"
    - "on map inference by mwss on perfect graphs"
    - "loopy belief propagation for approximate inference an empirical study"
    - "graphical models for game theory"
    - "message passing algorithms reparameterizations and splittings"
    - "the bethe permanent of a nonnegative matrix"

Connected through hyperedge HE-6 (induced by source paper "inference for generalized linear models via alternating directions and bethe free energy minimization"):
  with members:
    - "adaptive damping and mean removal for the generalized approximate message passing algorithm"
    - "an empirical bayes approach to recovering linearly constrained non negative sparse signals"
    - "bilinear generalized approximate message passing part i derivation"
    - "on the convergence of approximate message passing with arbitrary matrices"
    - "variational free energies for compressed sensing"
    - "sparse estimation with the swept approximated message passing algorithm"
    - "on convergence of approximate message passing"
    - "fixed points of generalized approximate message passing with arbitrary matrices"

Connected through hyperedge HE-7 (induced by source paper "fully connected deep structured networks"):
  with members:
    - "joint training of a convolutional network and a graphical model for human pose estimation"
    - "very deep convolutional networks for large scale image recognition"
    - "deep captioning with multimodal recurrent neural networks m rnn"
    - "learning deep structured models"
    - "long term recurrent convolutional networks for visual recognition and description"
    - "structured learning via logistic regression"
    - "imagenet large scale visual recognition challenge"
    - "from captions to visual concepts and back"

Connected through hyperedge HE-8 (induced by source paper "decomposition bounds for marginal map"):
  with members:
    - "message passing algorithms reparameterizations and splittings"
    - "convergent message passing algorithms for inference over general graphs with convex free energies"
    - "convergent message passing algorithms a unifying view"
    - "tightening lp relaxations for map using message passing"
    - "join graph based cost shifting schemes"
    - "solving map exactly using systematic search"
    - "a new class of upper bounds on the log partition function"
    - "tightening fractional covering upper bounds on the partition function for high order region graphs"

Question: Please tell me which class the center node 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)