1. Multivariate Gaussian Approximation for Random Forest via Region-based Stabilization
- Author
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Shi, Zhaoyang, Bhattacharjee, Chinmoy, Balasubramanian, Krishnakumar, and Polonik, Wolfgang
- Subjects
Mathematics - Statistics Theory ,Mathematics - Probability ,Statistics - Machine Learning - Abstract
We derive Gaussian approximation bounds for random forest predictions based on a set of training points given by a Poisson process, under fairly mild regularity assumptions on the data generating process. Our approach is based on the key observation that the random forest predictions satisfy a certain geometric property called region-based stabilization. In the process of developing our results for the random forest, we also establish a probabilistic result, which might be of independent interest, on multivariate Gaussian approximation bounds for general functionals of Poisson process that are region-based stabilizing. This general result makes use of the Malliavin-Stein method, and is potentially applicable to various related statistical problems.
- Published
- 2024