On the Convergence of CART under Sufficient Impurity Decrease Condition
Authors: Rahul Mazumder, Haoyue Wang
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we investigate the convergence rate of CART under a regression setting. First, we establish an upper bound on the prediction error of CART under a sufficient impurity decrease (SID) condition [10] our result improves upon the known result by [10] under a similar assumption. Furthermore, we provide examples that demonstrate the error bound cannot be further improved by more than a constant or a logarithmic factor. Second, we introduce a set of easily verifiable sufficient conditions for the SID condition. |
| Researcher Affiliation | Academia | Rahul Mazumder Sloan School of Management Massachusetts Institute of Technology rahulmaz@mit.edu Haoyue Wang Operations Research Center Massachusetts Institute of Technology haoyuew@mit.edu |
| Pseudocode | No | The paper describes the CART algorithm in detail in prose (Section 1.3) but does not include any pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not provide any statement or link indicating that source code for the described methodology is publicly available. |
| Open Datasets | No | The paper describes a synthetic dataset for an example: "Example 2.1 (Univariate linear function) Suppose p = 1, and xi are i.i.d. from the uniform distribution on [0, 1]." However, this is not a publicly available dataset with a link, DOI, or formal citation. |
| Dataset Splits | No | The paper uses a synthetic example but does not provide specific training/test/validation dataset splits or cross-validation details for it. |
| Hardware Specification | No | The paper does not explicitly describe the hardware used for the simulation presented in Figure 1. |
| Software Dependencies | No | The paper does not provide specific software dependencies or version numbers for the simulation conducted. |
| Experiment Setup | No | For the simulation in Example 2.1, the paper states "the depth d is taken as stated above (11)" which refers to a theoretical choice of `d = log2(n)/(1 log2(1 λ))`. This is a theoretical parameter choice rather than specific experimental setup details like learning rates, batch sizes, or optimizer settings typically found in an experimental setup description. |