Semi-Analytic Resampling in Lasso

Authors: Tomoyuki Obuchi, Yoshiyuki Kabashima

JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental To examine approximation accuracy and efficiency, numerical experiments were carried out using simulated datasets. Moreover, an application to a real-world dataset, the wine quality dataset, is presented.
Researcher Affiliation Academia Tomoyuki Obuchi EMAIL Yoshiyuki Kabashima EMAIL Department of Mathematical and Computing Science Tokyo Institute of Technology 2-12-1, Ookayama, Meguro-ku, Tokyo, Japan
Pseudocode No The paper describes the algorithm steps through a series of mathematical equations (21a-21j) and explanatory text, rather than a formally structured pseudocode block or an algorithm box.
Open Source Code Yes MATLAB codes implementing the proposed method are distributed in (Obuchi, 2018). (Reference: Tomoyuki Obuchi. Matlab package of AMPR. https://github.com/T-Obuchi/AMPR_lasso_matlab, 2018.)
Open Datasets Yes Moreover, an application to a real-world dataset, the wine quality dataset, is presented. (Reference: M. Lichman. UCI machine learning repository, 2013. URL http://archive.ics.uci.edu/ ml.)
Dataset Splits Yes To this end, we plot the solution paths and the generalization errors estimated by 10-fold cross validation (CV) in Figure 9 in the cases with and without the noise variables.
Hardware Specification Yes For reference, it should be noted that all experiments below were conducted in a single thread on a single CPU of Intel(R) Xeon(R) E5-2630 v3 2.4GHz.
Software Dependencies No For all experiments involving numerical resampling, Glmnet (Friedman et al., 2010), implemented as an MEX subroutine in MATLAB R , was employed for solving (9), given a sample {λ, Dc}. Moreover, the proposed AMPR algorithm was implemented as raw code in MATLAB. No specific version numbers for MATLAB or Glmnet are provided.
Experiment Setup Yes The other parameters are set to be (N, α, ρ0, σ2 ξ) = (1000, 0.5, 0.2, 0.01). (Figure 1 Caption) and To introduce correlations into the simulated dataset described above in a systematic way, we generate our covariates {xi}N i=1 in the following manner: As a common component we first generate a vector xcom RM each component of which is i.i.d. from N(0, 1/N); choose a number 0 rcom < 1 controlling the ratio of the common component and generate a binary vector mi each component of which independently takes 1 with probability rcom; take another vector xi RM each component of which is i.i.d. from N(0, 1/N), and generate a covariate vector xi as a linear combination between xcom and xi with using mi as a mask.