Gradient Boosting Performs Gaussian Process Inference

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. INTRODUCTION Gradient boosting (Friedman, 2001 ) is a classic machine learning algorithm successfully used for web search, recommendation systems, weather forecasting, and other problems (