Peng, Wei
(2021)
Asymptotic Normality and Rates of Convergence for Random Forests via Generalized U-statistics.
Doctoral Dissertation, University of Pittsburgh.
(Unpublished)
This is the latest version of this item.
Abstract
Random forests are among the most popular off-the-shelf supervised learning algorithms. Despite their well-documented empirical success, however, until recently, few theoretical results were available to describe their performance and behavior. In this work we push beyond recent work on consistency and asymptotic normality by establishing rates of convergence for random forests and other supervised learning ensembles. We develop the notion of generalized U-statistics and show that within this framework, random forest predictions can remain asymptotically normal for larger subsample sizes and under weaker conditions than previously established. Moreover, we provide Berry-Esseen bounds in order to quantify the rate at which this convergence occurs, making explicit the roles of the subsample size and the number of trees in determining the distribution of random forest predictions. When these generalized estimators are reduced to their classical U-statistic form, the rates we establish are faster than any available in the existing literature. We also provide a consistency estimate of the variance of random forest and illustrate that quantifying the uncertainty of random forest is typically more expensive than obtaining the random forest itself.
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Details
| Item Type: |
University of Pittsburgh ETD
|
| Status: |
Unpublished |
| Creators/Authors: |
|
| ETD Committee: |
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| Date: |
3 May 2021 |
| Date Type: |
Publication |
| Defense Date: |
26 March 2021 |
| Approval Date: |
3 May 2021 |
| Submission Date: |
6 April 2021 |
| Access Restriction: |
No restriction; Release the ETD for access worldwide immediately. |
| Number of Pages: |
113 |
| Institution: |
University of Pittsburgh |
| Schools and Programs: |
Dietrich School of Arts and Sciences > Statistics |
| Degree: |
PhD - Doctor of Philosophy |
| Thesis Type: |
Doctoral Dissertation |
| Refereed: |
Yes |
| Uncontrolled Keywords: |
random forests, generalized U-statistics, asymptotic normality, Berry-Esseen bound, variance estimation |
| Date Deposited: |
03 May 2021 15:28 |
| Last Modified: |
03 May 2021 15:28 |
| URI: |
http://d-scholarship.pitt.edu/id/eprint/40809 |
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