Implicit Regularization for Optimal Sparse Recovery
Authors: Tomas Vaskevicius, Varun Kanade, Patrick Rebeschini
NeurIPS 2019 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We validate our findings with numerical experiments and compare our algorithm against explicit 1 penalization. |
| Researcher Affiliation | Academia | 1 Department of Statistics, 2 Department of Computer Science University of Oxford |
| Pseudocode | Yes | Algorithm 1. Let α, η > 0 be two given parameters. Let u0 = v0 = α and for all t 0 we let mt = 1. Perform the updates given in (1). Algorithm 2. Let α, τ N and w max ˆz 2w max be three given parameters. Set η = 1 20ˆz and u0 = v0 = α. Perform the updates in (1) with m0 = 1 and mt adaptively defined as follows: 1. Set mt = mt 1. 2. If t = mτ log α 1 for some natural number m 2 then let mt,j = 2mt 1,j for all j such that u2 t,j v2 t,j 2 m 1ˆz. |
| Open Source Code | No | The paper does not provide any concrete access information (e.g., a link or explicit statement) for its own source code. |
| Open Datasets | No | The paper describes generating synthetic data for its simulations: "For each run the entries of X are sampled as i.i.d. Rademacher random variables and the noise vector ξ follows i.i.d. N(0, σ2) distribution." It does not use or provide access to any publicly available dataset. |
| Dataset Splits | Yes | Among the 200 obtained models we choose the one with the smallest error on a validation dataset of size n/4. |
| Hardware Specification | No | The paper does not provide any specific hardware details (e.g., GPU/CPU models, memory specifications) used for running its experiments. |
| Software Dependencies | No | The paper does not provide specific software dependencies with version numbers (e.g., libraries, frameworks, or programming language versions). |
| Experiment Setup | Yes | Unless otherwise specified, the default values for simulation parameters are n = 500, d = 104, k = 25, α = 10 12, γ = 1, σ = 1 and for Algorithm 2 we set τ = 10. |