Sharp analysis of power iteration for tensor PCA
Authors: Yuchen Wu, Kangjie Zhou
JMLR 2024 | Venue PDF | Archive PDF | Plain Text | 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 . |