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.