How rotational invariance of common kernels prevents generalization in high dimensions
Authors: Konstantin Donhauser, Mingqi Wu, Fanny Yang
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In this section we describe our synthetic and real-world experiments to further illustrate our theoretical results and underline the importance of feature selection in high dimensional kernel learning. |
| Researcher Affiliation | Academia | 1Department of Computer Science, ETH Z urich. Correspondence to: Konstantin Donhauser <donhausk@ethz.ch>. |
| Pseudocode | No | No pseudocode or algorithm blocks were found in the paper. |
| Open Source Code | No | The paper does not provide any specific links or explicit statements about the release of open-source code for the described methodology. |
| Open Datasets | Yes | In this section we show results on the regression dataset residential housing (RH) with n = 372 and d = 107 to predict sales prices from the UCI website (Dua and Graff, 2017). |
| Dataset Splits | Yes | We use a random 80/20 train/test split, and the data is scaled to zero mean and unit variance for each dimension separately. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models) used for running the experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers. |
| Experiment Setup | Yes | We primarily use the Laplace kernel with τ = tr(Σd) unless otherwise specified and study two sparse monomials as ground truth functions, f 1 (x) = 2x2 (1) and f 2 (x) = 2x3 (1)... In order to estimate the bias EY ˆf0 f 2 L2(PX) of the minimum norm interpolant we fit noiseless observations and approximate the expected squared error using 10000 i.i.d. test samples. |