Affine Rank Minimization via Asymptotic Log-Det Iteratively Reweighted Least Squares
Authors: Sebastian Krämer
JMLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Lastly, we analyze several presented aspects empirically in a series of numerical experiments. In particular, allowing for instance sufficiently many iterations, one may even observe a phase transition for generic recoverability at the absolute theoretical minimum. |
| Researcher Affiliation | Academia | Sebastian Kr amer EMAIL Institut f ur Geometrie und Praktische Mathematik RWTH Aachen University Aachen, 52062, Germany |
| Pseudocode | Yes | Algorithm 1 Asymptotic Minimization 1: set X(0) L 1(y) and γ(0) > 0 2: for i = 1, 2, . . . do 3: X(i) := Ψγ(i 1)(X(i 1)) 4: set γ(i) γ(i 1) according to chosen strategy Algorithm 2 (one-sided, matrix) IRLS-p 1: set p [0, 1], X(0) L 1(y) and γ(0) > 0 (cf. Proposition 14) 2: for i = 1, 2, . . . do 3: W (i 1) := (X(i 1)X(i 1)T + γ(i 1)I)p/2 1 4: X(i) := argmin X L 1(y) W (i 1)1/2X F (cf. (13)) 5: set γ(i) γ(i 1) according to chosen strategy |
| Open Source Code | Yes | The Matlab code behind all results is available as public repository under the name a-irls. |
| Open Datasets | No | Each measurement vector is constructed via a (not necessarily sought for) rank rrs N reference solution, which in turn relies on a randomly generated low-rank decomposition, y = L(X(rs)) Rℓ, X(rs) = Y (rs)Z(rs) Rn m, Y (rs) Rn rrs, Z(rs) Rrrs m. All entries of the two components Y (rs) and Z(rs) are assigned independent, normally distributed entries. The paper generates synthetic data for its experiments rather than using publicly available datasets, thus no access information for a pre-existing dataset is provided. |
| Dataset Splits | No | The paper describes generating synthetic data for each experiment, rather than using a pre-existing dataset with fixed train/test/validation splits. For example, 'Each measurement vector is constructed via a (not necessarily sought for) rank rrs N reference solution, which in turn relies on a randomly generated low-rank decomposition'. Therefore, specific dataset split information in the traditional sense is not applicable or provided. |
| Hardware Specification | No | The paper does not provide specific hardware details such as GPU models, CPU types, or memory used for running the experiments. |
| Software Dependencies | No | The paper mentions 'The Matlab code behind all results' but does not specify the version of Matlab or any other software libraries with their version numbers. |
| Experiment Setup | Yes | Based on a sufficiently large starting value γ(0) > 0, we by default choose γ(i) = νγ(i 1), i N, where ν < 1 remains constant throughout each single run of an algorithm. If not otherwise specified, the default weight strength, as it is our main interest, is given through p = 0. Experiment 16: 'Each constellation is repeated 1000 times for kmax = 12.' Experiment 17: 'Each constellation is repeated 1000 times for the increased value kmax = 14 (with ν14 1.00001 1).' Sensitivity Analysis: 'For each instance, we lower the meta parameter ν = νk = νk 1 (cf. Section 5.1.2), starting with ν0 = 1.2, and rerun the respective algorithm from the start until the result is not a failure, or, if after too many reruns k > kmax, we give up and thus either achieve a weak or strong failure depending on the result for k = kmax.' |