Subspace Embedding and Linear Regression with Orlicz Norm

Authors: Alexandr Andoni, Chengyu Lin, Ying Sheng, Peilin Zhong, Ruiqi Zhong

ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Finally, we complement our theoretical results with experimental evaluation of our algorithms. Our experiments reveal that that the solution of regression under the Orlicz norm induced by Huber loss is much better than the solution given by regression under ℓ1 or ℓ2 norms, under natural noise distributions in practice. We also perform experiments for Orlicz regression with different Orlicz functions G and show their behavior under different noise settings, thus exhibiting the flexibility of our framework.
Researcher Affiliation Academia 1Computer Science Department, Columbia University, New York City, NY 10027, U.S.A..
Pseudocode Yes Algorithm 1 Linear regression with Orlicz norm G
Open Source Code No The paper does not provide any statements about the availability of open-source code for the described methodology.
Open Datasets Yes Then, we run experiments on real datasets diabetes and glass in UCI repository(Bache & Lichman, 2013).
Dataset Splits No The paper mentions using simulated data and real datasets but does not provide specific details on training, validation, or test splits (e.g., percentages, sample counts, or citations to standard splits).
Hardware Specification No The paper does not provide specific hardware details (e.g., GPU/CPU models, memory) used for running the experiments.
Software Dependencies No The paper states 'We use MATLAB s linprog to solve ℓ1 regression.' However, it does not specify version numbers for MATLAB or the linprog function, which is insufficient for reproducible software dependencies.
Experiment Setup Yes We chose the parameter δ to be 0.75. In all the simulations, we generate matrix A Rn d, ground truth x Rd, and b to be Ax plus some particular noise. We experiment with two n, d combinations, i) n = 200, d = 10 ii) n = 100, d = 75, and 3 noise setting with i) Gaussian noise ii) sparse noise and iii) mixed noise (addition of i) and ii)), altogether 2 3 = 6 setting.