Sparse GCA and Thresholded Gradient Descent
Authors: Sheng Gao, Zongming Ma
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We also demonstrate the prowess of the algorithm on a number of synthetic data sets. ... This section reports numerical results on synthetic data sets. ... Table 1 reports the results of the aforementioned simulation study. For all latent dimensions, we observe a significant decrease in estimation error after Algorithm 1 is applied. ... From Figure 1, we observe an approximate linear decay trend at the beginning in all cases, which corresponds to exponential decay in the original scale. Moreover, after sufficiently many iterations, all error curves plateau, which suggests that the performance of the resulting estimators have stabilized. Both phenomena agree well with the theoretical findings in Theorem 7. |
| Researcher Affiliation | Academia | Sheng Gao EMAIL Zongming Ma EMAIL Department of Statistics and Data Science University of Pennsylvania Philadelphia, PA 19104, USA |
| Pseudocode | Yes | Algorithm 1: Thresholded gradient descent for sparse GCA Input: Covariance matrix estimator bΣ and its block diagonal part bΣ0; Initialization b A0. Tuning Parameters: Step size η; Penalty λ; Sparsity level s ; Number of iterations T; |
| Open Source Code | No | The paper does not provide concrete access to source code for the methodology described. There is no explicit statement about code release, nor are there any repository links or mentions of code in supplementary materials. |
| Open Datasets | No | This section reports numerical results on synthetic data sets. ... To generate covariance matrices Σ and Σ0, we use the latent variable model specified in Section 2. ... To generate U{i} Rpi r, we first randomly select a support of size 5. |
| Dataset Splits | Yes | The procedure for the selection of s is as follows. We first randomly split the data X into five folds of equal sizes. For l = 1, . . . , 5, we use one fold as the test set Xtest (l) and the other four folds combined as the training set Xtrain (l) . |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., GPU/CPU models, processor types, memory amounts) used for running its experiments. It describes numerical studies but omits hardware specifications. |
| Software Dependencies | No | The paper does not provide specific ancillary software details (e.g., library or solver names with version numbers) needed to replicate the experiments. Only conceptual algorithms and mathematical frameworks are discussed. |
| Experiment Setup | Yes | For tuning parameters in Algorithm 1, we set s = 20, η = 0.001, λ = 0.01, and T = 15000. The tuning parameter for generalized Fantope initialization is set to be n . The truncation parameter for initialization is also set to be s = 20. |