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].
Optimal Structured Principal Subspace Estimation: Metric Entropy and Minimax Rates
Authors: Tony Cai, Hongzhe Li, Rong Ma
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | This paper presents a unified framework for the statistical analysis of a general structured principal subspace estimation problem which includes as special cases sparse PCA/SVD, non-negative PCA/SVD, subspace constrained PCA/SVD, and spectral clustering. General minimax lower and upper bounds are established to characterize the interplay between the information-geometric complexity of the constraint set for the principal subspaces, the signal-to-noise ratio (SNR), and the dimensionality. The results yield interesting phase transition phenomena concerning the rates of convergence as a function of the SNRs and the fundamental limit for consistent estimation. |
| Researcher Affiliation | Academia | Tony Cai EMAIL Department of Statistics University of Pennsylvania Philadelphia, PA 19104, USA Hongzhe Li EMAIL Department of Biostatistics, Epidemiology and Informatics University of Pennsylvania Philadelphia, PA 19104, USA Rong Ma EMAIL Department of Biostatistics, Epidemiology and Informatics University of Pennsylvania Philadelphia, PA 19104, USA |
| Pseudocode | Yes | 1. Multiplication: Gt = YY Ut; 2. QR factorization: U t+1Wt+1 = Gt where U t+1 is p1 r orthonormal and Wt+1 is r r upper triangular; 3. Projection: Ut+1 = PC(U t+1). |
| Open Source Code | No | The paper does not provide any specific links to source code repositories, nor does it contain explicit statements about the release of source code for the methodology described. |
| Open Datasets | No | The paper is theoretical and does not conduct experiments that use specific datasets. Therefore, it does not mention any publicly available or open datasets. |
| Dataset Splits | No | The paper is theoretical and does not conduct experiments on datasets. Consequently, there are no mentions of training/test/validation dataset splits. |
| Hardware Specification | No | The paper is theoretical and focuses on mathematical analysis and proofs, rather than empirical experiments. As such, no hardware specifications for running experiments are provided. |
| Software Dependencies | No | The paper is theoretical and does not describe computational experiments or implementations that would require specific software dependencies with version numbers. It mentions general solvers like CPLEX, Gecode, and Choco in a discussion of algorithms, but not as software used by the authors for this paper's results. |
| Experiment Setup | No | The paper is theoretical and focuses on establishing minimax rates and bounds, not on conducting empirical experiments. Therefore, it does not include details on experimental setup such as hyperparameters or system-level training settings. |