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].
Consensus-Based Optimization on the Sphere: Convergence to Global Minimizers and Machine Learning
Authors: Massimo Fornasier, Lorenzo Pareschi, Hui Huang, Philippe Sünnen
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We present several numerical experiments, which show that the algorithm proposed in the present paper scales well with the dimension and is extremely versatile. To quantify the performances of the new approach, we show that the algorithm is able to perform essentially as good as ad hoc state of the art methods in challenging problems in signal processing and machine learning, namely the phase retrieval problem and the robust subspace detection. |
| Researcher Affiliation | Academia | Massimo Fornasier EMAIL Department of Mathematics Technical University of Munich Boltzmannstraße 3, 85748 Garching (Munich), Germany Hui Huang EMAIL Department of Mathematics Technical University of Munich Boltzmannstraße 3, 85748 Garching (Munich), Germany Lorenzo Pareschi EMAIL Department of Mathematics & Computer Science University of Ferrara Via Machiavelli 30, Ferrara, 44121, Italy Philippe S unnen EMAIL Department of Mathematics Technical University of Munich Boltzmannstraße 3, 85748 Garching (Munich), Germany |
| Pseudocode | Yes | Algorithm 1: KV-CBO Input: t, σ, α, d, N, n T and the function E( ) 1 Generate V i 0, i = 1, . . . , N sample vectors uniformly on Sd 1; 2 for n = 0 to n T do 3 Generate Bi n independent normal random vectors N(0, t); 4 Compute V α,E n ; 5 V i n+1 V i n+ t P(V i n)V α,E n +σ|V i n V α,E n |P(V i n) Bi n tσ2 2 (V i n V α,E n )2(d 1)V i n, V i n+1 V i n+1/| V i n+1|, i = 1, . . . , N; |
| Open Source Code | Yes | For the sake of reproducible research, in the repository https://github.com/Philippe Su/KV-CBO we provide the Matlab code, which implements the algorithms on the test cases of this paper. |
| Open Datasets | Yes | For the robust subspace detection we test the algorithm also in dimension d 3000 on the Adult Faces Database (Bainbridge et al., 2013) for the computation of eigenfaces. |
| Dataset Splits | No | The paper mentions using a |
| Hardware Specification | No | The authors acknowledge the support and the facilities of the LRZ Compute Cloud of the Leibniz Supercomputing Center of the Bavarian Academy of Sciences, on which the numerical experiments of this paper have been tested. |
| Software Dependencies | No | For the comparsion we used the Matlab toolbox Phase Pack (Chandra et al., 2017) and our own code. |
| Experiment Setup | Yes | We report in Figure 2 the particle trajectories for t [0, 5] in the case of N = 20, t = 0.05, σ = 0.25 and α = 50. On the left we consider the case with minimum at v = (0, 0, 1)T , on the right the case with minimum at v = (1/ 2, 1/2, 1/2)T . The time evolution of the particle distribution ρ(v, t) in the numerical mean field limit for N = 106 is also reported in the upper part of the same figure. |