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arXiv Machine Learning By Luis A. Ortega, Andr\'es R. Masegosa, Thomas D. Nielsen

Generalized Matheron Variational Implicit Processes

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Generalized Matheron Variational Implicit Processes (GMVIP) provide a pathwise variational family for posterior inference with implicit-process priors, such as Bayesian neural networks and stochastic simulators. For Gaussian‑process priors, GMVIP reproduces the standard inducing‑variable variational GP construction, while for general implicit priors it preserves the prior mean and covariance in the population limit. The method constructs posterior samples by drawing a function from the prior and applying a correction anchored at inducing inputs, with the correction determined directly from prior samples, and achieves a tractable coefficient‑space Kullback‑Leibler divergence. Experiments on regression, classification, and forecasting demonstrate that GMVIP is broadly competitive with existing methods.

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