Gaussian Process Training with Input Noise

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Manifold Gaussian Processes for regression (2014, background): “This kind of GP training is also analytically intractable, although approximations exist (Lawrence, 2005; Wang et al., 2008; McHutchon and Rasmussen, 2011; Titsias and Lawrence, 2010).”
Gaussian Processes for Data-Efficient Learning in Robotics and Control (2015, neutral): “approaches for training GPs with noise on both the training inputs and training targets yield initial promising results [36].”
Probabilistic Recurrent State-Space Models (2018, methodology): “Therefore, results are detailed for GP-NARX, NIGP, RE-VARB 1, and REVARB 2 for all combinations of normalized/unnormalized training data and mean or moment matching predictions.”
Recent Advances in Bayesian Optimization (2022, background): “McHutchon and Rasmussen [170] pointed out that the effect of the input-dependent noise is related to the gradient of the function mapping input to output.”
Active Learning of Linear Embeddings for Gaussian Processes (2013, background): “Unlike the work of McHutchon & Rasmussen (2011), giving an existing approach to GP regression with uncertain inputs, the Gaussian over the inputs here is correlated; the location of a datum is correlated with all others via mutual dependence on R .”