Cut-Pursuit Algorithm for Regularizing Nonsmooth Functionals with Graph Total Variation
Authors: Hugo Raguet, Loic Landrieu
ICML 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | The performance of our algorithm, which we demonstrate on difficult, ill-conditioned large-scale inverse and learning problems, is such that it may in practice extend the scope of application of the total-variation regularization. |
| Researcher Affiliation | Academia | 1LIVE, CNRS, Univ. Strasbourg, France 2Univ. Paris-Est, La STIG MATIS, IGN, ENSG, F-94160 Saint-Mandé, France. |
| Pseudocode | Yes | Algorithm 1 Principle of the cut-pursuit; D RV is a set of directions adapted to the problem. initialize V {V }; repeat find ξ(V) RV, stationary point of F (V) : ξ 7 F P U V ξU1U ; x P U V ξ(V) U 1U; find d(x) D, minimizing d 7 F (x, d); V S U V maximal constant connected components of d(x) u u U ; until F (x, d(x)) 0; return x. |
| Open Source Code | Yes | The source code for CP and PFDR is available at one of the author s Git Hub repository.2 1a7r0ch3/CP_PFDR_graph_d1 |
| Open Datasets | Yes | Fortunately, following Becker et al. (2014), a reasonable assumption is that at a given time, only scarce regions of the brain are really activated, and that spatially neighboring regions are often similarly activated. |
| Dataset Splits | No | The paper describes stopping criteria for the optimization process and refers to “medium- and large-scale problems” but does not specify training, validation, or test dataset splits with percentages, counts, or explicit mention of a validation set. |
| Hardware Specification | No | The paper discusses computational efficiency and running times but does not provide specific hardware details, such as CPU or GPU models, or memory specifications, used for conducting the experiments. |
| Software Dependencies | No | The paper mentions comparing with “state-of-the-art proximal splitting methods” like PFDR and PPD, but it does not list specific software libraries or their version numbers that were used for implementation or experimentation (e.g., Python, PyTorch, specific solvers). |
| Experiment Setup | Yes | Following his methodology, we prescribe stopping criteria as minimum relative evolution of the iterates, decreasing from 10 4 to 10 6; for the reduced problems in CP, the stopping criterion is set to one thousandth of this value. We also consider longer runs of the algorithms with a stopping criterion of 10 8 for CP and stopped after 105 iterations for PPD and PFDR. |