Orbit Regularization
Authors: Renato Negrinho, Andre Martins
NeurIPS 2014 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We describe the results of numerical experiments when regularizing with the permutahedron (symmetric group) and the signed permutahedron (hyperoctahedral group). All problems were solved using the conditional gradient algorithm, as described in 5. We generated the true model bw Rd by sampling the entries from a uniform distribution in [0, 1] and subtracted the mean, keeping k d nonzeros; after which bw was normalized to have unit ℓ2-norm. Then, we sampled a random nby-d matrix X with i.i.d. Gaussian entries and variance σ2 = 1/d, and simulated measurements y = X bw + n, where n N(0, σ2 n) is Gaussian noise. We set d = 500 and σn = 0.3σ. |
| Researcher Affiliation | Collaboration | Renato Negrinho Instituto de Telecomunicac oes Instituto Superior T ecnico 1049 001 Lisboa, Portugal renato.negrinho@gmail.com Andr e F. T. Martins Instituto de Telecomunicac oes Instituto Superior T ecnico 1049 001 Lisboa, Portugal atm@priberam.pt Also at Priberam Labs, Alameda D. Afonso Henriques, 41 2 , 1000 123, Lisboa, Portugal. |
| Pseudocode | Yes | 1: Initialize w1 = 0 2: for t = 1, 2, . . . do 3: ut = arg maxu Gv L(wt), u 4: ηt = 2/(t + 2) 5: wt+1 = (1 ηt)wt + ηtut 6: end for (Figure 2: Conditional gradient (left) and projected gradient (right) algorithms.) |
| Open Source Code | No | The paper does not provide any statement or link indicating that the source code for the described methodology is publicly available. |
| Open Datasets | No | The paper states: "We generated the true model bw Rd by sampling the entries from a uniform distribution in [0, 1]..." and "Then, we sampled a random nby-d matrix X with i.i.d. Gaussian entries...". This indicates synthetic data generation, but no access information (link, DOI, citation) is provided for a publicly available or open dataset. |
| Dataset Splits | No | The paper mentions: "this constant, and the regularization constants for ℓ1 and ℓ2, were all chosen with validation in a held-out set". While a held-out set is mentioned for validation, specific details such as percentages, sample counts, or explicit split methodology are not provided. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., GPU/CPU models, memory) used for running the experiments. |
| Software Dependencies | No | The paper does not mention any specific software dependencies with version numbers (e.g., library names like PyTorch 1.9, or solver versions like CPLEX 12.4) that are needed to reproduce the experiments. |
| Experiment Setup | Yes | We set d = 500 and σn = 0.3σ. ... Here, we fixed n = 250 and k = 300 and ran the continuation algorithm with ϵ = 0.1 and α = 0.0, for 5 different initializations of v0. |