Coherent Matrix Completion
Authors: Yudong Chen, Srinadh Bhojanapalli, Sujay Sanghavi, Rachel Ward
ICML 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We further provide extensive numerical evidence that a proposed two-phase sampling algorithm can perform nearly as well as local-coherence sampling and without requiring a priori knowledge of the matrix coherence structure. 4.1. Numerical experiments We now analyze the performance of the two-phase sampling procedure outlined in Algorithm 1 through numerical experiments. |
| Researcher Affiliation | Academia | Yudong Chen YDCHEN@UTEXAS.EDU University of California, Berkeley, CA 94720, USA Srinadh Bhojanapalli BSRINADH@UTEXAS.EDU Sujay Sanghavi SANGHAVI@MAIL.UTEXAS.EDU Rachel Ward RWARD@MATH.UTEXAS.EDU The University of Texas at Austin, Austin, TX 78712, USA |
| Pseudocode | Yes | Algorithm 1 Two-phase sampling for coherent matrix completion input Sampled matrix P (M), rank parameter r, and m, β such that | | = βm. 1: Compute the rank-r SVD of P (M), U V >. 2: Estimate the local coherences by µi = n1 3: Generate a set of (1 β)m new samples distributed as pij = min ( µi+ j)r log2(n1+n2) min{n1,n2} , 1 4: M = arg min k Xk s.t P [ (X) = P [ (M). output Completed matrix M. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code for the methodology described, nor does it provide a link to a code repository. |
| Open Datasets | No | For this, we consider rank-5 matrices of size 500 500 of the form M = DUV >D, where the entries of matrices U and V are i.i.d. Gaussian N(0, 1) and D is a diagonal matrix with power-law decay, Dii = i , 1 i 500. We refer to such constructions as power-law matrices. |
| Dataset Splits | No | The paper does not provide specific dataset split information (exact percentages, sample counts, or detailed splitting methodology) for training, validation, or testing. The experiments involve sampling from synthetically generated matrices rather than using pre-split datasets. |
| Hardware Specification | No | The paper does not provide specific hardware details (exact GPU/CPU models, processor types, or memory amounts) used for running its experiments. |
| Software Dependencies | No | The paper mentions using 'an Augmented Lagrangian Method (ALM) based solver by (Chen & Ganesh, 2009)' but does not provide specific version numbers for this or any other software dependencies needed to replicate the experiment. |
| Experiment Setup | Yes | For this, we consider rank-5 matrices of size 500 500 of the form M = DUV >D, where the entries of matrices U and V are i.i.d. Gaussian N(0, 1) and D is a diagonal matrix with power-law decay, Dii = i , 1 i 500. We refer to such constructions as power-law matrices. Successful recovery is defined as when at least 95% of trials have relative error in the Frobenius norm not exceeding 0.01. The above simulations are run with two-phase parameter β = 2/3. |