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 "maximum likelihood estimation of functionals of discrete distributions"):
  Abstract: We consider the problem of estimating functionals of discrete distributions, and focus on tight nonasymptotic analysis of the worst case squared error risk of widely used estimators. We apply concentration inequalities to analyze the random fluctuation of these estimators around their expectations, and the theory of approximation using positive linear operators to analyze the deviation of their expectations from the true functional, namely their \emph{bias}. #R##N#We characterize the worst case squared error risk incurred by the Maximum Likelihood Estimator (MLE) in estimating the Shannon entropy $H(P) = \sum_{i = 1}^S -p_i \ln p_i$, and $F_\alpha(P) = \sum_{i = 1}^S p_i^\alpha,\alpha>0$, up to multiplicative constants, for any alphabet size $S\leq \infty$ and sample size $n$ for which the risk may vanish. As a corollary, for Shannon entropy estimation, we show that it is necessary and sufficient to have $n \gg S$ observations for the MLE to be consistent. In addition, we establish that it is necessary and sufficient to consider $n \gg S^{1/\alpha}$ samples for the MLE to consistently estimate $F_\alpha(P), 0<\alpha<1$. The minimax rate-optimal estimators for both problems require $S/\ln S$ and $S^{1/\alpha}/\ln S$ samples, which implies that the MLE has a strictly sub-optimal sample complexity. When $1<\alpha<3/2$, we show that the worst-case squared error rate of convergence for the MLE is $n^{-2(\alpha-1)}$ for infinite alphabet size, while the minimax squared error rate is $(n\ln n)^{-2(\alpha-1)}$. When $\alpha\geq 3/2$, the MLE achieves the minimax optimal rate $n^{-1}$ regardless of the alphabet size. #R##N#As an application of the general theory, we analyze the Dirichlet prior smoothing techniques for Shannon entropy estimation. We show that no matter how we tune the parameters in the Dirichlet prior, this technique cannot achieve the minimax rates in entropy estimation.

Includes members:
  Member "estimation of kl divergence optimal minimax rate":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "out of distribution detection with distance guarantee in deep generative models")
  Member "minimax rate optimal estimation of divergences between discrete distributions":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "credible sample elicitation")
  Member "adaptive estimation of shannon entropy":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "importance of small probability events in big data information measures applications and challenges")
  Member "justification of logarithmic loss via the benefit of side information":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "on the information bottleneck problems models connections applications and information theoretic views")
  Member "minimax estimation of functionals of discrete distributions":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "on the information bottleneck problems models connections applications and information theoretic views")
  Member "minimax rates of entropy estimation on large alphabets via best polynomial approximation":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "to split or not to split the impact of disparate treatment in classification")
  Member "estimating renyi entropy of discrete distributions":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "practical estimation of renyi entropy")

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.IT(Information Theory)