Summary of Statistical-computational Trade-offs For Recursive Adaptive Partitioning Estimators, by Yan Shuo Tan et al.
Statistical-Computational Trade-offs for Recursive Adaptive Partitioning Estimators
by Yan Shuo Tan, Jason M. Klusowski, Krishnakumar Balasubramanian
First submitted to arxiv on: 7 Nov 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Data Structures and Algorithms (cs.DS); Machine Learning (cs.LG); Statistics Theory (math.ST)
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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 This paper explores the limitations of models based on recursive adaptive partitioning, such as decision trees and their ensembles, in high-dimensional regression tasks. Specifically, it examines the performance of greedy algorithms used to train these models, which are often computationally infeasible due to empirical risk minimization (ERM). The researchers show that when the true regression function does not satisfy a certain property called the Merged Staircase Property (MSP), greedy training requires an exponential number of samples to achieve low estimation error. However, if the true regression function satisfies MSP, greedy training can achieve small estimation error with only a logarithmic number of samples. This dichotomy is similar to that observed in two-layer neural networks trained with stochastic gradient descent (SGD) in the mean-field regime. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In simple terms, this paper looks at how well models like decision trees do when trying to learn from high-dimensional data. They found out that these models can be slow and inefficient if they’re not designed correctly. The researchers also discovered a connection between their findings and another type of machine learning model called neural networks. |
Keywords
» Artificial intelligence » Machine learning » Regression » Stochastic gradient descent
