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.