Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Low Permutation-rank Matrices: Structural Properties and Noisy Completion
Authors: Nihar B. Shah, Sivaraman Balakrishnan, Martin J. Wainwright
JMLR 2019 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | We establish the minimax rates of estimation under the new permutation-based model, and prove that surprisingly, the minimax rates are equivalent up to logarithmic factors to those for estimation under the typical low rank model. Third, we analyze a computationally efficient singular-value-thresholding algorithm, known to be optimal for the low-rank setting, and show that it also simultaneously yields a consistent estimator for the low-permutation rank setting. Finally, we present various structural results characterizing the uniqueness of the permutation-rank decomposition, and characterizing convex approximations of the permutation-rank polytope. |
| Researcher Affiliation | Academia | Nihar B. Shah EMAIL Machine Learning Department and Computer Science Department Carnegie Mellon University Sivaraman Balakrishnan EMAIL Department of Statistics Carnegie Mellon University Martin J. Wainwright EMAIL EECS Department and Department of Statistics University of California, Berkeley |
| Pseudocode | No | The paper describes algorithms like Singular Value Thresholding (SVT) and outlines their operational steps in prose, for example: 'From the observation matrix Y {0, 1 2, 1}n d, we first obtain the transformed observation matrix Y as in equation (2a). Applying the singular value decomposition yields the representation Y = UDV T...'. However, it does not include any explicitly labeled pseudocode blocks or algorithms in a structured, code-like format. |
| Open Source Code | No | No explicit statements regarding the release of source code, such as 'We release our code...' or links to code repositories (e.g., GitHub), are present in the paper. The mention of 'License: CC-BY 4.0' pertains to the publication itself, not the availability of code for the described methodology. |
| Open Datasets | No | The paper uses a 'recommender system application' as a running example to illustrate its modeling, describing hypothetical scenarios such as 'n 2 users and d 2 items, as well as an unknown matrix M [0, 1]n d that captures the users preferences for the items.' This description refers to a conceptual model and problem setting rather than a specific, real-world dataset used for empirical evaluation. No specific dataset names, download links, DOIs, or citations to publicly available datasets are provided. |
| Dataset Splits | No | The paper does not present any empirical experiments that would involve data. Consequently, there is no mention of dataset splits (e.g., training, validation, or test sets) or methodologies for partitioning data. |
| Hardware Specification | No | The paper is theoretical in nature, focusing on mathematical models, rates of estimation, and algorithm analysis. It does not describe any computational experiments or benchmarks that would necessitate the use or specification of particular hardware components (e.g., CPU, GPU, memory). As such, no hardware specifications are provided. |
| Software Dependencies | No | The paper focuses on theoretical analysis and algorithms, such as Singular Value Thresholding (SVT), but does not discuss the implementation details or list specific software libraries, frameworks, or their version numbers that would be required to replicate any experiments. For instance, there is no mention of programming languages (e.g., Python, R), machine learning libraries (e.g., TensorFlow, PyTorch), or statistical packages with their corresponding versions. |
| Experiment Setup | No | The paper is a theoretical work that focuses on mathematical proofs, properties of models, and algorithm analysis, rather than empirical evaluation. Therefore, it does not describe any experimental setup details, such as specific hyperparameter values (e.g., learning rates, batch sizes), model initialization, training schedules, or any other configuration parameters typically found in papers reporting experimental results. |