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: "hamiltonian variational auto encoder"
  Abstract: Variational Auto-Encoders (VAEs) have become very popular techniques to perform inference and learning in latent variable models as they allow us to leverage the rich representational power of neural networks to obtain flexible approximations of the posterior of latent variables as well as tight evidence lower bounds (ELBOs). Combined with stochastic variational inference, this provides a methodology scaling to large datasets. However, for this methodology to be practically efficient, it is necessary to obtain low-variance unbiased estimators of the ELBO and its gradients with respect to the parameters of interest. While the use of Markov chain Monte Carlo (MCMC) techniques such as Hamiltonian Monte Carlo (HMC) has been previously suggested to achieve this [23, 26], the proposed methods require specifying reverse kernels which have a large impact on performance. Additionally, the resulting unbiased estimator of the ELBO for most MCMC kernels is typically not amenable to the reparameterization trick. We show here how to optimally select reverse kernels in this setting and, by building upon Hamiltonian Importance Sampling (HIS) [17], we obtain a scheme that provides low-variance unbiased estimators of the ELBO and its gradients using the reparameterization trick. This allows us to develop a Hamiltonian Variational Auto-Encoder (HVAE). This method can be reinterpreted as a target-informed normalizing flow [20] which, within our context, only requires a few evaluations of the gradient of the sampled likelihood and trivial Jacobian calculations at each iteration.

Connected through hyperedge HE-1 (induced by source paper "pi vae encoding stochastic process priors with variational autoencoders"):
  with members:
    - "an introduction to variational autoencoders"
    - "exact gaussian processes on a million data points"
    - "quality of uncertainty quantification for bayesian neural network inference"
    - "attentive neural processes"
    - "conditional neural processes"
    - "gpytorch blackbox matrix matrix gaussian process inference with gpu acceleration"
    - "adam a method for stochastic optimization"
    - "expectation propagation for approximate bayesian inference"

Connected through hyperedge HE-2 (induced by source paper "energy inspired models learning with sampler induced distributions"):
  with members:
    - "implicit generation and generalization in energy based models"
    - "divide and couple using monte carlo variational objectives for posterior approximation"
    - "importance weighting and variational inference"
    - "kernel exponential family estimation via doubly dual embedding"
    - "noise contrastive estimation and negative sampling for conditional models consistency and statistical efficiency"
    - "learning descriptor networks for 3d shape synthesis and analysis"
    - "stochastic video generation with a learned prior"
    - "representation learning with contrastive predictive coding"

Connected through hyperedge HE-3 (induced by source paper "exponential family estimation via adversarial dynamics embedding"):
  with members:
    - "implicit generation and generalization in energy based models"
    - "kernel exponential family estimation via doubly dual embedding"
    - "spectral normalization for generative adversarial networks"
    - "monge amp ere flow for generative modeling"
    - "ffjord free form continuous dynamics for scalable reversible generative models"
    - "calibrating energy based generative adversarial networks"
    - "improved training of wasserstein gans"
    - "density estimation using real nvp"

Connected through hyperedge HE-4 (induced by source paper "ergodic inference accelerate convergence by optimisation"):
  with members:
    - "importance weighted autoencoders"
    - "adam a method for stochastic optimization"
    - "hamiltonian annealed importance sampling for partition function estimation"

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.LG(Machine Learning)