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 "structure learning of h colorings"):
  Abstract: We study the structure learning problem for $H$-colorings, an important class of Markov random fields that capture key combinatorial structures on graphs, including proper colorings and independent sets, as well as spin systems from statistical physics. The learning problem is as follows: for a fixed (and known) constraint graph $H$ with $q$ colors and an unknown graph $G=(V,E)$ with $n$ vertices, given uniformly random $H$-colorings of $G$, how many samples are required to learn the edges of the unknown graph $G$? We give a characterization of $H$ for which the problem is identifiable for every $G$, i.e., we can learn $G$ with an infinite number of samples. We also show that there are identifiable constraint graphs for which one cannot hope to learn every graph $G$ efficiently. #R##N#We focus particular attention on the case of proper vertex $q$-colorings of graphs of maximum degree $d$ where intriguing connections to statistical physics phase transitions appear. We prove that in the tree uniqueness region (when $q>d$) the problem is identifiable and we can learn $G$ in ${\rm poly}(d,q) \times O(n^2\log{n})$ time. In contrast for soft-constraint systems, such as the Ising model, the best possible running time is exponential in $d$. In the tree non-uniqueness region (when $q\leq d$) we prove that the problem is not identifiable and thus $G$ cannot be learned. Moreover, when $q<d-\sqrt{d} + \Theta(1)$ we prove that even learning an equivalent graph (any graph with the same set of $H$-colorings) is computationally hard---sample complexity is exponential in $n$ in the worst case. We further explore the connection between the efficiency/hardness of the structure learning problem and the uniqueness/non-uniqueness phase transition for general $H$-colorings and prove that under the well-known Dobrushin uniqueness condition, we can learn $G$ in ${\rm poly}(d,q)\times O(n^2\log{n})$ time.

Includes members:
  Member "a dichotomy theorem for nonuniform csps":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "when symmetries are not enough a hierarchy of hard constraint satisfaction problems")
  Member "the proof of csp dichotomy conjecture":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "optimal polynomial time compression for boolean max csp")
  Member "approximately counting h colourings is bis hard":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lower bounds for testing graphical models colorings and antiferromagnetic ising models")
  Member "hardness of parameter estimation in graphical models":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "domain liftability of relational marginal polytopes")
  Member "maximum likelihood bounded tree width markov networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "efficient learning of optimal markov network topology with k tree modeling")
  Member "correlation decay up to uniqueness in spin systems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")
  Member "computational transition at the uniqueness threshold":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "spectral independence in high dimensional expanders and applications to the hardcore model")

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.DM(Discrete Mathematics)