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 "phase transitions for the uniform distribution in the pml problem and its bethe approximation"):
  Abstract: The pattern maximum likelihood (PML) estimate, introduced by Orlitsky et al., is an estimate of the multiset of probabilities in an unknown probability distribution p, the estimate being obtained from n i.i.d. samples drawn from p. The PML estimate involves solving a difficult optimization problem over the set of all probability mass functions (pmfs) of finite support. In this paper, we describe an interesting phase transition phenomenon in the PML estimate: at a certain sharp threshold, the uniform distribution goes from being a local maximum to being a local minimum for the optimization problem in the estimate. We go on to consider the question of whether a similar phase transition phenomenon also exists in the Bethe approximation of the PML estimate, the latter being an approximation method with origins in statistical physics. We show that the answer to this question is a qualified "Yes". Our analysis involves the computation of the mean and variance of the (i;j)th entry, ai;j , in a random k k non-negative integer matrix A with row and column sums all equal to M , drawn according to a distribution that assigns to A a probability proportional to Q i;j (M ai;j)!

Includes members:
  Member "the bethe permanent of a nonnegative matrix":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "gauges loops and polynomials for partition functions of graphical models")
  Member "counting in graph covers a combinatorial characterization of the bethe entropy function":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "pseudocodeword based decoding of quantum stabilizer codes")
  Member "on modeling profiles instead of values":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "differentially private anonymized histograms")
  Member "approximating the permanent with belief propagation":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "approximating the permanent by sampling from adaptive partitions")
  Member "belief propagation and beyond for particle tracking":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "approximating the permanent by sampling from adaptive partitions")

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)