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. |