Sparse Support Recovery with Non-smooth Loss Functions
Authors: Kévin Degraux, Gabriel Peyré, Jalal Fadili, Laurent Jacques
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | To exemplify the usefulness of our theory, we give a detailed numerical analysis of the support stability/instability of compressed sensing recovery with these different losses. This highlights different parameter regimes, ranging from total support stability to progressively increasing support instability. In Section 3, we propose numerical simulations to illustrate our theoretical findings on a compressed sensing (CS) scenario. Using Theorem 1, we are able to numerically assess the degree of support instability of CS recovery using ℓα fidelity. As a prelude to shed light on this result, we show on Figure 2, a smaller simulated CS example for (α, β) = ( , 1). |
| Researcher Affiliation | Academia | Kévin Degraux ISPGroup/ICTEAM, FNRS Université catholique de Louvain Louvain-la-Neuve, Belgium 1348 kevin.degraux@uclouvain.be Gabriel Peyré CNRS, DMA École Normale Supérieure Paris, France 75775 gabriel.peyre@ens.fr Jalal M. Fadili Normandie Univ, ENSICAEN, CNRS, GREYC, Caen, France 14050 Jalal.Fadili@ensicaen.fr Laurent Jacques ISPGroup/ICTEAM, FNRS Université catholique de Louvain Louvain-la-Neuve, Belgium 1348 laurent.jacques@uclouvain.be |
| Pseudocode | No | The paper does not contain any pseudocode or algorithm blocks. It focuses on mathematical derivations and numerical analysis. |
| Open Source Code | No | The paper mentions using "CVX/MOSEK [8, 7]" and provides a link to CVX: "http://cvxr.com/cvx". However, this is a link to a third-party tool used by the authors, not to the specific code implementation of their proposed methodology described in the paper. |
| Open Datasets | No | The paper states: "We set n = 1000, m = 900 and generate 200 times a random sensing matrix Φ Rm n with Φij i.i.d N(0, 1). For each sensing matrix, we generate 60 different k-sparse vectors x0 with support I where k def. = |I| varies from 10 to 600." This indicates the data was generated for the experiments and no public dataset was used with access information provided. |
| Dataset Splits | No | The paper describes numerical simulations where data is generated for each run. It does not mention any specific training, validation, or test dataset splits in terms of percentages or sample counts, nor does it refer to standard predefined splits. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory) used to run the experiments. It only mentions that 'All computations are done in Matlab'. |
| Software Dependencies | Yes | All computations are done in Matlab, using CVX [8, 7], with the MOSEK solver at best precision setting to solve the convex problems. [8] is 'CVX: Matlab software for disciplined convex programming, version 2.1.' |
| Experiment Setup | Yes | All computations are done in Matlab, using CVX [8, 7], with the MOSEK solver at best precision setting to solve the convex problems. We set n = 1000, m = 900 and generate 200 times a random sensing matrix Φ Rm n with Φij i.i.d N(0, 1). For each sensing matrix, we generate 60 different k-sparse vectors x0 with support I where k def. = |I| varies from 10 to 600. |