Notice: The reproducibility variables underlying each score are classified using an automated LLM-based pipeline, validated against a manually labeled dataset. LLM-based classification introduces uncertainty and potential bias; scores should be interpreted as estimates. Full accuracy metrics and methodology are described in [1].
Stochastic Proximal Methods for Non-Smooth Non-Convex Constrained Sparse Optimization
Authors: Michael R. Metel, Akiko Takeda
JMLR 2021 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | In a numerical experiment we compare our algorithms with the current state-of-the-art deterministic algorithm and find our algorithms to exhibit superior convergence. Keywords: stochastic optimization, non-convex optimization, non-smooth optimization, constrained optimization, sparse optimization |
| Researcher Affiliation | Academia | Michael R. Metel EMAIL Center for Artificial Intelligence Project, RIKEN Tokyo 103-0027, Japan Akiko Takeda EMAIL Graduate School of Information Science and Technology The University of Tokyo Tokyo 103-0027, Japan Center for Artificial Intelligence Project, RIKEN Tokyo 103-0027, Japan |
| Pseudocode | Yes | Algorithm 1 Mini-Batch Stochastic Proximal Algorithm (MBSPA) Input: w1 Rd, N Z>0, α, θ R M := Nα , λ = 1 Nθ Lλ = L + 1 λ, γ = 1 Lλ R uniform{1, ..., N} for k = 1, 2, ..., R 1 do ζλ(wk) proxλg(wk) Sample ξk P M Compute Ak λ,M(wk, ξk) (18) wk+1 = proxγh(wk γ Ak λ,M(wk, ξk)) end for Output: w R proxλg(w R) |
| Open Source Code | No | All parameters of SDCAM were left unchanged as used in the available implementation1. 1 http://www.mypolyuweb.hk/~tkpong/Matrix_sparse_MP_codes/ |
| Open Datasets | Yes | We test on the problem of non-negative sparse PCA (40) on datasets MNIST (Le Cun, 1998) and RCV1 (Lewis et al., 2004). |
| Dataset Splits | No | The dimensions of MNIST are n = 60, 000 and d = 784, and those of RCV1 are n = 804, 414 and d = 47, 236. |
| Hardware Specification | Yes | All experiments were conducted using MATLAB 2017b on a Mac Pro with a 2.7 GHz 12-core Intel Xeon E5 processor and 64GB of RAM. |
| Software Dependencies | Yes | All experiments were conducted using MATLAB 2017b on a Mac Pro with a 2.7 GHz 12-core Intel Xeon E5 processor and 64GB of RAM. |
| Experiment Setup | Yes | The values for α and θ established in Corollaries 10 and 15 were used to implement MBSPA and VRSPA. It was hypothesized that the inferior performance of VRSPA was due to its smaller stepsize, so VRSPA2 is VRSPA using the stepsize of MBSPA. All parameters of SDCAM were left unchanged as used in the available implementation1. The regularizer g(w) was chosen as MCP with parameters chosen as κ = 1/d and ν = 1. VRSPA requires that each fj(w) be L-smooth, so in our numerical experiments we took L = max j xjx j 2. We chose the number of iterations of each algorithm so that they terminate at approximately the same time where at least half of the algorithms reached an observable level of convergence. |