Matrix Completion with Hierarchical Graph Side Information
Authors: Adel Elmahdy, Junhyung Ahn, Changho Suh, Soheil Mohajer
NeurIPS 2020 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We conduct extensive experiments both on synthetic and real-world datasets to corroborate our theoretical results as well as to demonstrate significant performance improvements over other matrix completion algorithms that leverage graph side information. and 5 Experimental Results We first conduct Monte Carlo experiments to corroborate Theorem 1. Let α = eα log n n , β = eβ log n n , and γ = eγ log n n . We consider a setting where θ = 0.1, eβ = 10, eγ = 0.5, δg = δc = 0.5. The synthetic data is generated as per the model in Section 2. In Figs. 2a and 2b, we evaluate the performance of the proposed algorithm (with local iterative refinement of groups and rating vectors), and quantify the empirical success rate as a function of the normalized sample complexity, over 103 randomly drawn realizations of rating vectors and hierarchical graphs. We vary n and m, preserving the ratio n/m = 3. |
| Researcher Affiliation | Academia | Adel Elmahdy ECE, University of Minnesota adel@umn.edu Junhyung Ahn EE, KAIST tonyahn96@kaist.ac.kr Changho Suh EE, KAIST chsuh@kaist.ac.kr Soheil Mohajer ECE, University of Minnesota soheil@umn.edu |
| Pseudocode | Yes | Algorithm 1 Exact Recovery of Rating Vectors and Algorithm 2 Local Iterative Refinement of Groups (Set flag = 0) |
| Open Source Code | No | The paper does not provide an explicit statement or link for the open-source code of the methodology described within the paper. |
| Open Datasets | Yes | Next, similar to [41 44], the performance of the proposed algorithm is assessed on semi-real data (real graph but synthetic rating vectors). We consider a subgraph of the political blog network [80], which is shown to exhibit a hierarchical structure [50]. |
| Dataset Splits | No | The paper does not explicitly provide specific train/validation/test dataset splits, such as percentages, absolute sample counts, or references to predefined splits for its own experimental setup. It uses synthetic and semi-real data but does not detail how these were split for training/validation/testing. |
| Hardware Specification | No | The paper does not provide specific details about the hardware (e.g., CPU, GPU models, memory) used for running its experiments. |
| Software Dependencies | No | The paper mentions various algorithms and internal modifications but does not list specific software dependencies (e.g., programming languages, libraries, or solvers) with their version numbers. |
| Experiment Setup | Yes | Let α = eα log n n , β = eβ log n n , and γ = eγ log n n . We consider a setting where θ = 0.1, eβ = 10, eγ = 0.5, δg = δc = 0.5. The synthetic data is generated as per the model in Section 2. In Figs. 2a and 2b, we evaluate the performance of the proposed algorithm (with local iterative refinement of groups and rating vectors), and quantify the empirical success rate as a function of the normalized sample complexity, over 103 randomly drawn realizations of rating vectors and hierarchical graphs. We vary n and m, preserving the ratio n/m = 3. and We consider a tall matrix setting of n = 381 and m = 200... The corresponding rating vectors are generated such that the ratings are drawn from [0, 10] (i.e., real numbers), and the observations are corrupted by a Gaussian noise with mean zero and a given variance σ2. |