Collective Matrix Completion
Authors: Mokhtar Z. Alaya, Olga Klopp
JMLR 2019 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We further corroborate our theoretical findings through simulated experiments. In this section, we first provide algorithmic details of the numerical procedure for solving the problem (4), then we conduct experiments on synthetic data to further illustrate the theoretical results of the collective matrix completion. |
| Researcher Affiliation | Academia | Mokhtar Z. Alaya EMAIL Modal X, UPL, Univ Paris Nanterre, F92000 Nanterre France; Olga Klopp EMAIL ESSEC Business School and CREST, F95021 Cergy France |
| Pseudocode | Yes | Algorithm 1: APG for Collective Matrix Completion; Algorithm 2: Power Method: Power Method(Z, R, ϵ); Algorithm 3: Approximate SVT: Approx-SVT(Z, R, λ, δ); Algorithm 4: PLAIS-Impute for Collective Matrix Completion |
| Open Source Code | Yes | The code that generates all figures given below is available from https://github.com/mzalaya/collectivemc. |
| Open Datasets | No | In this section, we conduct experiments on synthetic data to further illustrate the theoretical results of the collective matrix completion. The paper describes how the synthetic data is generated but does not provide access information for it. |
| Dataset Splits | Yes | We randomly sample 80% of the observed entries for training, and the rest for testing. |
| Hardware Specification | Yes | The implementation of Algorithm 4 for the nuclear norm penalized estimator (4) was done in MATLAB R2017b on a desktop computer with mac OS system, Intel i7 Core 3.5 GHz CPU and 16GB of RAM. |
| Software Dependencies | Yes | The implementation of Algorithm 4 for the nuclear norm penalized estimator (4) was done in MATLAB R2017b on a desktop computer with mac OS system, Intel i7 Core 3.5 GHz CPU and 16GB of RAM. For fast computation of SVD and sparse matrix computations, the experiments call an external package called PROPACK (Larsen, 1998) implemented in C and Fortran. |
| Experiment Setup | Yes | In our experiments, the PLAIS-Impute algorithm terminates when the absolute difference in the cost function values between two consecutive iterations is less than ϵ = 10 6. We set the regularization parameter λ LY(M) as given by Theorem 3. We set the number of the source matrices V = 3, then, for each v {1, 2, 3}, the low-rank ground truth parameter matrices M v Rd dv are created with sizes d {3000, 6000, 9000} and dv {1000, 2000, 3000}. The parameter rv is set to {5, 10, 15}. A fraction of the entries of M v is removed uniformly at random with probability p [0, 1]. |