Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Fast Screening Rules for Optimal Design via Quadratic Lasso Reformulation
Authors: Guillaume Sagnol, Luc Pronzato
JMLR 2023 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The efficiency of the new screening rules and of the homotopy algorithm are demonstrated on different examples based on real data. |
| Researcher Affiliation | Academia | Guillaume Sagnol EMAIL Institut für Mathematik, Sekr. MA 5-2 Technische Universität Berlin, Straße des 17. Juni 136 10623 Berlin, Germany Luc Pronzato EMAIL Université Côte d Azur, CNRS, Laboratoire I3S 2000 route des lucioles 06900 Sophia Antipolis, France |
| Pseudocode | Yes | Algorithm 1 Homotopy algorithm for the quadratic lasso/c-optimal design. |
| Open Source Code | Yes | Last but not least, the code used in our experiments has been published in the form of a python package (qlasso) and is available at https://gitlab.com/gsagnol/qlasso. |
| Open Datasets | Yes | We use the training set of the well known MNIST database (Le Cun and Cortes, 2010) |
| Dataset Splits | No | For our purpose, we build a smaller training set of 600 images of each digit, which we arrange in a matrix A R784 6 000. ... The training set contains p = 1 200 images (there are 120 samples for each digit) |
| Hardware Specification | Yes | Calculations are in python on a PC at 2.7 GHz and 16 GB RAM. Calculations are in Matlab, on a PC with a clock speed of 2.5 GHz and 32 GB RAM |
| Software Dependencies | Yes | Table 1 compares the running time of the homotopy algorithm and CD with several first order algorithms (Multiplicative weight updates (MWU), FISTA, Frank-Wolfe (FW)), as well the time required by a commercial solver (Gurobi (Gurobi Optimization, LLC, 2023) used with the PICOS interface (Sagnol and Stahlberg, 2022) in Python) to solve two different Second-Order Cone Programming (SOCP) formulations of the problem. |
| Experiment Setup | Yes | The 10 support points of the optimal solution for λ = 0.4 are displayed in Figure 3 (left), together with the image corresponding to the vector c: as expected, all images represent the same digit (here, a six). Figure 2 shows the evolution of the duality gap Lλ(x) Dλ(y1(x)) for λ = 0.4, when the Coordinate Descent (CD) algorithm2 described in (Sagnol and Pauwels, 2019) is used (left), as well as the percentage of support points ρ(k) that have been eliminated after k iterations (right). ... For the above experiment, the CD algorithm was used as a reference because it performed better than first-order algorithms. Table 1 compares the running time of the homotopy algorithm and CD with several first order algorithms ... while we have used a tolerance of 10 4 for all other algorithms. We used the screening rule D1 with τ = 10 for CD, MWU, FISTA and FW. ... screening is computationally more efficient when applied periodically, every τ iterations, rather than at each k, and we use τ = 100 in the example. ... The algorithm is stopped when δ < 10 6 |