human: Given a node-centered hypergraph: <hypergraph>, where nodes represent papers and hyperedges represent sets of papers co-cited by a source paper.

Details of the hypergraph:
Center node: "how to find a joint probability distribution of minimum entropy almost given the marginals"
  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 the joint probability distribution in ${\cal C}({\bf p}, {\bf q})$ of minimum entropy (equivalently, the joint probability distribution that 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 by at most 1, thus providing an approximation algorithm with additive approximation factor of 1. 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 $X_1, \ldots , X_k$. In this case, our approximation algorithm has an additive approximation factor of $\log k$. We also discuss some related applications of our findings.

Connected through hyperedge HE-1 (induced by source paper "solving approximate wasserstein gans to stationarity"):
  with members:
    - "improving gans using optimal transport"
    - "the cramer distance as a solution to biased wasserstein gradients"
    - "which training methods for gans do actually converge"
    - "gans trained by a two time scale update rule converge to a nash equilibrium"
    - "near linear time approximation algorithms for optimal transport via sinkhorn iteration"
    - "the numerics of gans"
    - "improved training of wasserstein gans"
    - "gradient descent gan optimization is locally stable"

Connected through hyperedge HE-2 (induced by source paper "playing games with bounded entropy"):
  with members:
    - "entropic causal inference"
    - "on the entropy of couplings"
    - "on the hardness of entropy minimization and related problems"
    - "repeated matching pennies with limited randomness"

Question: Please tell me which class the center node 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)