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Abstract
Estimating distributional structures, such as density estimation and two-sample comparison, is
a fundamental task in data science. However, estimating high-dimensional distributions is widely
recognized as challenging due to the well-known curse of dimensionality. In the case of supervised
learning, where one needs to estimate an unknown function often defined on a high-dimensional
space, a common approach in statistics and machine learning is to introduce tree-based methods,
such as boosting, random forest, and Bayesian additive regression trees. These methods are known
to be effective for such challenging tasks with feasible computation costs. This presentation aims
to introduce their counterparts for unsupervised learning. We first introduce a new non-parametric
Bayesian model for learning distributions by generalizing the Polya tree process, which is originally
introduced for low-dimensional density estimation. We next propose a new way of combining
multiple tree-based learners in the manner of boosting for improved empirical performance.
This is joint work with Li Ma (Duke University).