Principal Component Hierarchy for Sparse Quadratic Programs
Authors: Robbie Vreugdenhil, Viet Anh Nguyen, Armin Eftekhari, Peyman Mohajerin Esfahani
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We benchmark different approaches to solve problem (P) in the sparse linear regression setting. All experiments are run on a laptop with Intel(R) Core(TM) i7-8750 CPU and 16GB RAM using MATLAB 2020b. The optimization problems are modeled using YALMIP (L ofberg, 2004), as the interface for the mixed-integer solver (MOSEK Ap S, 2019). Codes are available at: https://github.com/ RVreugdenhil/sparse QP |
| Researcher Affiliation | Collaboration | 1Delft Center for Systems and Control, Delft University of Technology 2Department of Management Science and Engineering, Stanford University 3Vin AI Research, Vietnam 4Department of Mathematics and Mathematical Statistics, Umea University. |
| Pseudocode | No | The paper describes algorithms (e.g., best response, dual program) in text and mathematical equations, but does not present them in a formalized pseudocode or algorithm block. |
| Open Source Code | Yes | Codes are available at: https://github.com/ RVreugdenhil/sparse QP |
| Open Datasets | Yes | for the UCI Superconductivity dataset1, we randomly select 70% of the dataset as training samples, and then compute the matrix Q, as specified in (2). 1Available at https://archive.ics.uci.edu/ml/ datasets/Superconductivty+Data. We benchmark different methods using real data sets (Dua & Graff, 2017); the details are listed in Table 3. |
| Dataset Splits | No | For each independent replication, we randomly sample 70% of the data as training data and 30% as test data. No explicit mention of a separate validation split or set was found. |
| Hardware Specification | Yes | All experiments are run on a laptop with Intel(R) Core(TM) i7-8750 CPU and 16GB RAM using MATLAB 2020b. |
| Software Dependencies | Yes | All experiments are run on a laptop with Intel(R) Core(TM) i7-8750 CPU and 16GB RAM using MATLAB 2020b. The optimization problems are modeled using YALMIP (L ofberg, 2004), as the interface for the mixed-integer solver (MOSEK Ap S, 2019). |
| Experiment Setup | Yes | To avoid a complicated terminating criterion, we run the BR method for TBR = 20 iterations, and we run the DP method for TDP = 500 iterations. The stepsize constant for DP (see Footnote 2) is set to a = 4 10 3. Regarding the post-processing step in Section 3.3, we fix p BR = 6 and p DP = 50 as the number of terminating solutions that are used to estimate the support Z. For the experiment on the synthetic data, the big-M constant is set to 4, because xtrue = 1. We choose the dimension of subspace k = 400. We fix the regularisation term η = 10. The number of iterations for the BR and DP are chosen to be TBR = 40 and TDP = 5000, respectively. The number of terminating solutions that are used to estimate the support Z in the postprocessing step is fixed to p BR = 10 and p DP = 100 for the two methods. The stepsize constant (see Footnote 2) is set a = 2 10 3. Moreover, we fix the big-M constant using the procedure described in Section 3.3. For the real datasets, the number of samples N is sufficiently bigger than the dimension n, thus we set the ridge regularization parameter to η = Ntrain so that the effect of regularization diminishes as N increases. We choose the sparsity level s = 10, similar to Section 4.1, and set the time limit for MOSEK to 300 seconds. |