New MCMC-based Wishart prior improves Gaussian Process learning

In supervised learning with Gaussian Processes (GPs), priors are typically placed on kernel hyperparameters, but when the function is highly multivariate, simultaneously learning multiple lengthscale parameters becomes computationally difficult. Kane Warrior and Dalia Chakrabarty propose a 'self-assembled' Wishart prior directly on the covariance matrix. They implement Bayesian inference via MCMC, using a look-back window over recent chain iterations to define a time-step dependent scale matrix. This introduces adaptiveness and helps diagnose weakly informative inputs within the GP learning paradigm.

Experimental results on both synthetic and real-world datasets show that this approach improves inference in high-dimensional settings. By directly modeling the correlation structure with a Wishart prior, the method can identify inputs that provide little signal, potentially leading to more robust and interpretable GP models. The work bridges advanced Bayesian computation and practical machine learning, offering a new tool for practitioners dealing with complex, multivariate regression tasks.