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 "optimum estimation via gradients of partition functions and information measures a statistical mechanical perspective"):
  Abstract: In continuation to a recent work on the statistical-mechanical analysis of minimum mean square error (MMSE) estimation in Gaussian noise via its relation to the mutual information (the I-MMSE relation), here we propose a simple and more direct relationship between optimum estimation and certain information measures (e.g., the information density and the Fisher information), which can be viewed as partition functions and hence are amenable to analysis using statistical-mechanical techniques. The proposed approach has several advantages, most notably, its applicability to general sources and channels, as opposed to the I-MMSE relation and its variants which hold only for certain classes of channels (e.g., additive white Gaussian noise channels). We then demonstrate the derivation of the conditional mean estimator and the MMSE in a few examples. Two of these examples turn out to be generalizable to a fairly wide class of sources and channels. For this class, the proposed approach is shown to yield an approximate conditional mean estimator and an MMSE formula that has the flavor of a single-letter expression. We also show how our approach can easily be generalized to situations of mismatched estimation.

Includes members:
  Member "statistical physics of signal estimation in gaussian noise theory and examples of phase transitions":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "understanding phase transitions via mutual information and mmse")
  Member "threshold effects in parameter estimation as phase transitions in statistical mechanics":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "lower bounds on parameter modulation estimation under bandwidth constraints")
  Member "rate distortion function via minimum mean square error estimation":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "a survey on mimo transmission with discrete input signals technical challenges advances and future trends")
  Member "how could the replica method improve accuracy of performance assessment of channel coding":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "error exponents of typical random codes for the colored gaussian channel")
  Member "life above threshold from list decoding to area theorem and mse":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "low density majority codes and the problem of graceful degradation")
  Member "mutual information and minimum mean square error in gaussian channels":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "on the information bottleneck problems models connections applications and information theoretic views")

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)