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 Coakley et alK. L. Coakley, T. Snelleman, H. Hoos, and O. E. Gundersen, "The embrace of open science: An analysis of a decade of AI research and 56 800 conference papers," Under Review, 2026..
Sharp analysis of power iteration for tensor PCA
Authors: Yuchen Wu, Kangjie Zhou
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Extensive numerical experiments verify our theoretical results. Keywords: Spiked model, tensor PCA, power iteration, approximate message passing, non-convex optimization |
| Researcher Affiliation | Academia | Yuchen Wu EMAIL Department of Statistics and Data Science University of Pennsylvania Philadelphia, PA 19104-6303, USA Kangjie Zhou EMAIL Department of Statistics Stanford University Stanford, CA 94305-2004, USA |
| Pseudocode | No | The paper describes the tensor power iteration algorithm mathematically and analyzes its dynamics, but does not present it in a structured pseudocode or algorithm block. For example, 'Tensor power iteration initialized at v0 is defined recursively as follows: vt+1 = T[( vt) (k 1)] = λn v, vt k 1v + W [( vt) (k 1)], vt+1 = vt+1 vt+1 2 , (2)' is a mathematical definition. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing source code or links to code repositories. |
| Open Datasets | No | The numerical experiments use synthetically generated tensor data according to a model, not a publicly available dataset. For example, 'generate the tensor data according to Eq. (1).' and 'For each tensor realization, we run tensor power iteration from a random initialization...' |
| Dataset Splits | No | The paper uses synthetically generated data for numerical experiments, repeating the process '1000 times independently' for various configurations. This approach does not involve predefined training/test/validation splits of a fixed dataset. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running the numerical experiments, such as CPU or GPU models, or cloud computing specifications. |
| Software Dependencies | No | The paper does not mention any specific software or library versions used for implementation or experiments (e.g., Python, PyTorch, TensorFlow, or specific numerical libraries with versions). |
| Experiment Setup | Yes | To set the stage, we choose n = 200, k = 3, λn = n(k 1)/2, and generate the tensor data according to Eq. (1). We then run tensor power iteration with random initialization and compare the marginal distributions of αt and Xt, for all t {1, 2, 3, 4}. We repeat this procedure 1000 times independently, and collect the realized values of αt to form the corresponding empirical distributions. ... For this part we let λn = n(k 1)/2, k = 3, and use different values of n. For each n {25, 50, 100, 200, 400, 800}, we repeat this procedure independently for 1000 times and compute the empirical convergence probability. ... Tstop := inf t N+ : vt 2, vt 3 1/2 . |