Wasserstein Gradient Boosting: A General Framework with Applications to Posterior Regression

Gradient boosting is a sequential ensemble method that fits a new base learner to the gradient of the remaining loss at each step. We propose a novel family of gradient boosting, Wasserstein gradient boosting, which fits a new base learner to an exactly or approximately available Wasserstein gradient of a loss functional on the space of probability distributions. Wasserstein gradient boosting returns a set of particles that approximates a target probability distribution assigned at each input. In probabilistic prediction, a parametric probability distribution is often specified on the space of output variables, and a point estimate of the output-distribution parameter is produced for each input by a model. Our main application of Wasserstein gradient boosting is a novel distributional estimate of the output-distribution parameter, which approximates the posterior distribution over the output-distribution parameter determined pointwise at each data point. We empirically demonstrate the superior performance of the probabilistic prediction by Wasserstein gradient boosting in comparison with various existing methods.