Gradient Boosting Performs Gaussian Process Inference

Aleksei Ustimenko, Artem Beliakov, Liudmila Prokhorenkova

Keywords: gradient boosting, gaussian process, knowledge uncertainty, kernel gradient boosting

TL;DR: We prove that gradient boosting converges to a Gaussian process' posterior mean and can be transformed into a sampler from the posterior, which leads to improved knowledge uncertainty estimates.

Abstract: This paper shows that gradient boosting based on symmetric decision trees can be equivalently reformulated as a kernel method that converges to the solution of a certain Kernel Ridge Regression problem. Thus, we obtain the convergence to a Gaussian Process' posterior mean, which, in turn, allows us to easily transform gradient boosting into a sampler from the posterior to provide better knowledge uncertainty estimates through Monte-Carlo estimation of the posterior variance. We show that the proposed sampler allows for better knowledge uncertainty estimates leading to improved out-of-domain detection.

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