High-Dimensional Interactions Detection with Sparse Principal Hessian Matrix
Authors: Cheng Yong Tang, Ethan X. Fang, Yuexiao Dong
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Numerical examples including simulation and a real data example are presented in Section 4 to demonstrate the promising performance of the method. In this section, we conduct extensive numerical studies to demonstrate and validate the performance of our proposed method. |
| Researcher Affiliation | Academia | Cheng Yong Tang EMAIL Department of Statistical Science Fox School of Business Temple University Philadelphia, PA 19122-6083, USA Ethan X. Fang EMAIL Department of Statistics Pennsylvania State University University Park, PA 16801, USA Yuexiao Dong EMAIL Department of Statistical Science Fox School of Business Temple University Philadelphia, PA 19122-6083, USA |
| Pseudocode | Yes | Algorithm 1 ADMM Algorithm to Estimate Ψ |
| Open Source Code | No | The paper does not explicitly state that source code for the methodology is openly available or provide a link to a repository. |
| Open Datasets | Yes | We further apply the proposed method to analyze the GPL96 microarray dataset analyzed in Mc Call et al. (2010); Wu et al. (2013); Fang et al. (2017). |
| Dataset Splits | Yes | We treat the disease status as responses, and randomly split the dataset into a training set and a testing set. Each training set contains 100 samples from the breast tumor group and 150 samples from the normal group. |
| Hardware Specification | Yes | In all tables, we report the averaged running time in seconds, where all experiments are conducted on an iMac with 3.2 GHz Intel Core i5 Processor and 16 GB memory. |
| Software Dependencies | No | No specific software dependencies with version numbers are mentioned in the paper. |
| Experiment Setup | Yes | In our simulation setup, we fix the sample size as n = 100, and we consider different dimensions for p = 100, 200 and 300. Meanwhile, we generate the design matrix X = (x1, x2, ..., xn)T Rn p by generating each sample xi Rp independently from a pdimensional Gaussian distribution X N(0, Σ), where the covariance matrix Σ is either the identity matrix, or a Toeplitz matrix, i.e. Σjk = ρ|j k| for some ρ (0, 1). We then generate the noises ϵi s independently from a normal random variable N(0, σ2), and we consider different σ s. ... We choose the tuning parameter by 10-fold cross-validation. ... Each training set contains 100 samples from the breast tumor group and 150 samples from the normal group. We repeat the random split 100 times. |