Fast Projected Newton-like Method for Precision Matrix Estimation under Total Positivity
Authors: Jian-Feng CAI, José Vinícius de Miranda Cardoso , Daniel Palomar, Jiaxi Ying
NeurIPS 2023 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Experimental results on synthetic and real-world datasets demonstrate that our proposed algorithm provides a significant improvement in computational efficiency compared to the state-of-the-art methods. We conduct experiments on synthetic and real-world data to verify the performance of our algorithm. |
| Researcher Affiliation | Academia | Hong Kong University of Science and Technology1 HKUST Shenzhen-Hong Kong Collaborative Innovation Research Institute2 |
| Pseudocode | Yes | Algorithm 1 Fast Projected Newton-like (FPN) algorithm |
| Open Source Code | No | The paper does not provide any statement or link indicating that the source code for the methodology is openly available. |
| Open Datasets | Yes | The concepts dataset [43], from Intel Labs, comprises 1000 nodes and 218 semantic features, with p = 1000 and n = 218. Reference [43]: B. Lake and J. Tenenbaum, Discovering structure by learning sparse graphs, in Proceedings of the 33rd Annual Cognitive Science Conference, 2010, pp. 778 783. |
| Dataset Splits | No | The paper focuses on estimating precision matrices given i.i.d. observations. It does not describe or use traditional train/validation/test dataset splits for model training or hyperparameter tuning. |
| Hardware Specification | Yes | All experiments were conducted on 2.10GHZ Xeon Gold 6152 machines and Linux OS |
| Software Dependencies | No | All methods were implemented in MATLAB. (No specific version number for MATLAB is provided) |
| Experiment Setup | Yes | We set the regularization parameter λij in Problem (1) as follows λij = σ [ ˆ X]ij + ϵ , i = j, where ˆ X represents an estimator, ϵ is set to 10 3, and σ > 0 is a parameter that adjusts the sparsity. For PQN-LBFGS, we utilize the previous 50 updates to compute the search direction. For FPN, we set ϵk = 10 15 in (8) for identifying the set of restricted variables. |