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: "convex calibration dimension for multiclass loss matrices"
  Abstract: We study consistency properties of surrogate loss functions for general multiclass learning problems, defined by a general multiclass loss matrix. We extend the notion of classification calibration, which has been studied for binary and multiclass 0-1 classification problems (and for certain other specific learning problems), to the general multiclass setting, and derive necessary and sufficient conditions for a surrogate loss to be calibrated with respect to a loss matrix in this setting. We then introduce the notion of convex calibration dimension of a multiclass loss matrix, which measures the smallest `size' of a prediction space in which it is possible to design a convex surrogate that is calibrated with respect to the loss matrix. We derive both upper and lower bounds on this quantity, and use these results to analyze various loss matrices. In particular, we apply our framework to study various subset ranking losses, and use the convex calibration dimension as a tool to show both the existence and non-existence of various types of convex calibrated surrogates for these losses. Our results strengthen recent results of Duchi et al. (2010) and Calauzenes et al. (2012) on the non-existence of certain types of convex calibrated surrogates in subset ranking. We anticipate the convex calibration dimension may prove to be a useful tool in the study and design of surrogate losses for general multiclass learning problems.

Connected through hyperedge HE-1 (induced by source paper "an embedding framework for consistent polyhedral surrogates"):
  with members:
    - "on the consistency of top k surrogate losses"
    - "on structured prediction theory with calibrated convex surrogate losses"
    - "analysis and optimization of loss functions for multiclass top k and multilabel classification"
    - "general truthfulness characterizations via convex analysis"
    - "learning with submodular functions a convex optimization perspective"

Connected through hyperedge HE-2 (induced by source paper "toward a characterization of loss functions for distribution learning"):
  with members:
    - "faster and sample near optimal algorithms for proper learning mixtures of gaussians"
    - "learning mixtures of structured distributions over discrete domains"

Connected through hyperedge HE-3 (induced by source paper "quantifying learning guarantees for convex but inconsistent surrogates"):
  with members:
    - "on structured prediction theory with calibrated convex surrogate losses"
    - "exponential convergence of testing error for stochastic gradient methods"
    - "a consistent regularization approach for structured prediction"
    - "on the consistency of ordinal regression methods"
    - "saga a fast incremental gradient method with support for non strongly convex composite objectives"
    - "minimizing the misclassification error rate using a surrogate convex loss"

Connected through hyperedge HE-4 (induced by source paper "sharp analysis of learning with discrete losses"):
  with members:
    - "a consistent regularization approach for structured prediction"
    - "on the consistency of ordinal regression methods"
    - "a theoretical analysis of ndcg type ranking measures"

Connected through hyperedge HE-5 (induced by source paper "on structured prediction theory with calibrated convex surrogate losses"):
  with members:
    - "a consistent regularization approach for structured prediction"
    - "training deep neural networks via direct loss minimization"
    - "simultaneous model selection and optimization through parameter free stochastic learning"
    - "on the consistency of ordinal regression methods"
    - "surrogate regret bounds for bipartite ranking via strongly proper losses"

Connected through hyperedge HE-6 (induced by source paper "on the consistency of ordinal regression methods"):
  with members:
    - "a hybrid loss for multiclass and structured prediction"
    - "agnostic learning of monomials by halfspaces is hard"

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.LG(Machine Learning)