Towards Faster Rates and Oracle Property for Low-Rank Matrix Estimation

Authors: Huan Gui, Jiawei Han, Quanquan Gu

ICML 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental Extensive numerical experiments on both synthetic and real world datasets corroborate our theoretical findings.
Researcher Affiliation Academia Huan Gui HUANGUI2@ILLINOIS.EDU Jiawei Han HANJ@ILLINOIS.EDU Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, IL 61801, USA Quanquan Gu* QG5W@VIRGINIA.EDU Department of Systems and Information Engineering, University of Virginia, Charlottesville, VA 22904, USA
Pseudocode Yes Algorithm 1 t=1 PGH(λ0, λtgt, opt, Lmin); Algorithm 2 { e , b L} Prox Grad(λ,b , 0, L0); Algorithm 3 { , N} Line Search(λ, M, L)
Open Source Code No The paper does not provide concrete access to source code for the methodology described.
Open Datasets Yes The Jester dataset can be downloaded from http://eigentaste.berkeley.edu/dataset/. The images can be downloaded from http://www.utdallas.edu/ cxc123730/mh_bcs_spl.html.
Dataset Splits No The paper mentions selecting 50% of data as observations and the remaining 50% for predictions, but does not explicitly specify a separate validation set or typical train/validation/test splits.
Hardware Specification No The paper does not provide specific hardware details used for running its experiments.
Software Dependencies No The paper does not provide specific ancillary software details with version numbers.
Experiment Setup Yes We study the performance of estimators with both convex and nonconvex penalties for m 2 {40, 60, 80}, and the rank r = blog2 mc. Xi s are uniformed sampled over X, with the variance of observation noise σ2 = 0.25. For every configuration, we repeat 100 trials and compute the averaged mean squared Frobenius norm error k b k2F /m2 over all trials. For matrix sensing, we set the rank r = 10 for all m 2 {20, 40, 80}. ... We set the observation noise variance σ2 = 1 and = I, i.e., the entries of Xi are independent. Each setting is repeated for 100 times. ... We project the underlying matrices into the corresponding subspaces associated with the top r = 200 singular values of each matrix... In addition, we randomly select 50% of the entries as observations. Each trial is repeated 10 times. ... We randomly select 50% of the ratings as observations, and make predictions over the remaining 50%. Each run is repeated for 10 times.