Summary of Regression Trees Know Calculus, by Nathan Wycoff
Regression Trees Know Calculus
by Nathan Wycoff
First submitted to arxiv on: 22 May 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Regression tree models have become a popular tool for solving real-world regression problems due to their ability to handle nonlinearities, interaction effects, and sharp discontinuities. This paper explores the relationship between node parameters in regression trees and the local gradient of the function being approximated when applied to well-behaved, differentiable functions. The authors propose a simple estimate of the gradient that can be efficiently computed using quantities exposed by popular tree learning libraries. This enables the integration of tools developed for differentiable algorithms, such as neural networks and Gaussian processes, with regression trees. To demonstrate this, the paper studies measures of model sensitivity defined in terms of integrals of gradients and shows how to compute them for regression trees using the proposed gradient estimates. The authors perform quantitative and qualitative numerical experiments that reveal the capability of estimated gradients to improve predictive analysis, solve tasks in uncertainty quantification, and provide interpretation of model behavior. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper is about a type of computer model called regression tree. These models are good at solving real-world problems because they can handle complicated relationships between things. The researchers looked at how these models work when dealing with simple, smooth functions. They found a way to estimate the direction in which the function changes (called the gradient) using information from the model. This allows them to use tools developed for other types of computer models (like neural networks and Gaussian processes) with regression trees. The researchers tested their idea by doing some math problems and showed that it works well. |
Keywords
» Artificial intelligence » Regression
