Generalization Bounds for Inductive Matrix Completion in Low-Noise Settings
Authors: Antoine Ledent, Rodrigo Alves, Yunwen Lei, Yann Guermeur, Marius Kloft
AAAI 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experiments In this paper, we have posited that an accurate understanding of the sample complexity landscape of inductive matrix completion requires treating the noise component differently from the ground truth entries for the purposes of complexity. In this section we present the experiments we ran to confirm that a two-phase phenomenon as suggested by our bounds does in fact occur in practice. We considered random matrices of size 100 ˆ 100 and of rank 101, and created random orthonormal side information of rank 40, ensuring that the singular vectors of the ground truth matrix are in the span of the relevant side information, but with the orientation being otherwise uniformly random. The ground truth matrices were normalized to have Frobenius norm 100, and we then added i.i.d. Np0, σ2q gaussian noise to each observation. We performed classic inductive matrix completion (with the square loss) on the resulting training set, cross-validating the parameter λ on a validation set, and evaluated the RMSE distance between the resulting trained matrix and the ground truth. We performed this whole procedure for a wide range of different values for the number of samples N. For each value of N we perform the procedure on 40 different random matrix and side information. |
| Researcher Affiliation | Academia | Antoine Ledent1*, Rodrigo Alves2, Yunwen Lei3, Yann Guermeur4, and Marius Kloft5 1 Singapore Management University (SMU) 2 Czech Technical University in Prague (CTU) 3 Hong Kong Baptist University (HKBU) 4 Centre National de la Recherche Scientique (CNRS) 5 Technische Universität Kaiserslautern (TUK) |
| Pseudocode | No | The paper describes algorithms and proof strategies in narrative text and mathematical formulations, but it does not contain explicitly labeled 'Pseudocode' or 'Algorithm' blocks with structured steps. |
| Open Source Code | No | The paper does not contain any explicit statements or links indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The paper describes generating 'synthetic data experiments' (random matrices, random orthonormal side information, and i.i.d. gaussian noise) rather than using an existing publicly available dataset, and no access information (link, DOI, or citation) is provided for this generated data. |
| Dataset Splits | No | The paper mentions using a 'training set' and 'validation set' and describes 'cross-validating the parameter λ on a validation set', but it does not specify the exact percentages or methodology (e.g., random seed, stratified splitting) of these dataset splits. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU/CPU models, memory) used to run the experiments. |
| Software Dependencies | No | The paper does not list any specific software components or libraries with their version numbers that were used in the experiments. |
| Experiment Setup | No | The paper mentions 'cross-validating the parameter λ' but does not provide specific experimental setup details such as concrete hyperparameter values (e.g., learning rate, batch size) or other training configurations. |