Efficient Algorithms for Non-convex Isotonic Regression through Submodular Optimization
Authors: Francis Bach
NeurIPS 2018 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We consider experiments aiming at (a) showing that the new possibility of minimizing submodular functions with isotonic constraints brings new possibilities and (b) that the new discretization algorithms are faster than the naive one. |
| Researcher Affiliation | Academia | Francis Bach Inria Département d Informatique de l Ecole Normale Supérieure PSL Research University, Paris, France francis.bach@ens.fr |
| Pseudocode | Yes | All pseudo-codes for the algorithms are available in Appendix B. |
| Open Source Code | No | The paper states that pseudocodes are available in Appendix B, but it does not provide any explicit statement or link for the open-source code of the described methodology. |
| Open Datasets | No | We generate the data z ∈ Rn, with n = 200, as follows: we first generate a simple decreasing function of i ∈ {1, . . . , n} (here an affine function); we then perturb this ground truth by (a) adding some independent noise and (b) corrupting the data by changing a random subset of the n values by the application of another function which is increasing. The paper generates its own data and does not provide access information for a publicly available dataset. |
| Dataset Splits | No | The paper describes data generation for its experiments but does not specify training/validation/test splits for any dataset, nor does it mention cross-validation or other common splitting methodologies. |
| Hardware Specification | No | The paper does not provide any specific hardware details such as CPU models, GPU models, or memory specifications used for running the experiments. |
| Software Dependencies | No | The paper mentions using a 'standard max-flow code [5]' and discusses algorithms like Dykstra's, but it does not provide specific version numbers for any software dependencies. |
| Experiment Setup | Yes | For simplicity, we consider chain constraints 1 > x1 > x2 > ... > xn > 0. We consider two set-ups: (a) a separable set-up where maximum flow algorithms can be used directly (with n = 200), and (b) a general submodular set-up (with n = 25 and n = 200), where we add a smoothness penalty which is the sum of terms of the form λ Σi=1 (xi − xi+1)2. We solve the discretized version by a single maximum-flow problem of size nk. We compare the various losses for k = 1000 on data which is along a decreasing line (plus noise), but corrupted (i.e., replaced for a certain proportion) by data along an increasing line. |