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Deep Gaussian Process (DGP) models offer a powerful nonparametric approachfor Bayesian inference, but exact inference is typically intractable,motivating the use of various approximations. However, existing approaches,such as mean-field Gaussian assumptions, limit the expressiveness and efficacyof DGP models, while stochastic approximation can be computationally expensive.To tackle these challenges, we introduce Neural Operator Variational Inference(NOVI) for Deep Gaussian Processes. NOVI uses a neural generator to obtain asampler and minimizes the Regularized Stein Discrepancy in L2 space between thegenerated distribution and true posterior. We solve the minimax problem usingMonte Carlo estimation and subsampling stochastic optimization techniques. Wedemonstrate that the bias introduced by our method can be controlled bymultiplying the Fisher divergence with a constant, which leads to robust errorcontrol and ensures the stability and precision of the algorithm. Ourexperiments on datasets ranging from hundreds to tens of thousands demonstratethe effectiveness and the faster convergence rate of the proposed method. Weachieve a classification accuracy of 93.56 on the CIFAR10 dataset,outperforming SOTA Gaussian process methods. Furthermore, our method guaranteestheoretically controlled prediction error for DGP models and demonstratesremarkable performance on various datasets. We are optimistic that NOVI has thepotential to enhance the performance of deep Bayesian nonparametric models andcould have significant implications for various practical applications

Neural Operator Variational Inference based on Regularized Stein Discrepancy for Deep Gaussian Processes