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 "minimum entropy couplings and their applications"):
  Abstract: Given two discrete random variables $X$ and $Y,$ with probability distributions ${\bf p}=(p_1, \ldots , p_n)$ and ${\bf q}=(q_1, \ldots , q_m)$, respectively, denote by ${\cal C}({\bf p}, {\bf q})$ the set of all couplings of ${\bf p}$ and ${\bf q}$, that is, the set of all bivariate probability distributions that have ${\bf p}$ and ${\bf q}$ as marginals. In this paper, we study the problem of finding a joint probability distribution in ${\cal C}({\bf p}, {\bf q})$ of \emph{minimum entropy} (equivalently, a coupling that \emph{maximizes} the mutual information between $X$ and $Y$), and we discuss several situations where the need for this kind of optimization naturally arises. Since the optimization problem is known to be NP-hard, we give an efficient algorithm to find a joint probability distribution in ${\cal C}({\bf p}, {\bf q})$ with entropy exceeding the minimum possible at most by {1 bit}, thus providing an approximation algorithm with an additive gap of at most 1 bit. Leveraging on this algorithm, we extend our result to the problem of finding a minimum--entropy joint distribution of arbitrary $k\geq 2$ discrete random variables $X_1, \ldots , X_k$, consistent with the known $k$ marginal distributions of the individual random variables $X_1, \ldots , X_k$. In this case, our algorithm has an { additive gap of at most $\log k$ from optimum.} #R##N#We also discuss several related applications of our findings and {extensions of our results to entropies different from the Shannon entropy.}

Includes members:
  Member "strong functional representation lemma and applications to coding theorems":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "communication for generating correlation a unifying survey")
  Member "bounds on the entropy of a function of a random variable and their applications":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "on data processing and majorization inequalities for f divergences with applications")
  Member "mutual information bounds via adjacency events":
    also connected through other hyperedges:
      (none)
  Member "entropic causal inference":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "counterfactual off policy evaluation with gumbel max structural causal models")
  Member "on the entropy of couplings":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "asymptotic coupling and its applications in information theory")
  Member "sumset and inverse sumset inequalities for differential entropy and mutual information":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "countably infinite multilevel source polarization for non stationary erasure distributions")
  Member "entropic inequalities and marginal problems":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "information theoretic inference of common ancestors")
  Member "entropy bounds for discrete random variables via maximal coupling":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "asymptotic finite sample information losses in neural classifiers")

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)