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