Convex Programming for Estimation in Nonlinear Recurrent Models
Authors: Sohail Bahmani, Justin Romberg
JMLR 2020 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We evaluate the performance of the estimator by simulation on synthetic data. These numerical experiments also suggest the extent at which the imposed theoretical assumptions may be relaxed. |
| Researcher Affiliation | Academia | Sohail Bahmani EMAIL School of Electrical & Computer Engineering Georgia Institute of Technology Atlanta, GA 30332 Justin Romberg EMAIL School of Electrical & Computer Engineering Georgia Institute of Technology Atlanta, GA 30332 |
| Pseudocode | No | The paper includes mathematical formulations, theorems, and proofs but does not contain any clearly labeled pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not contain any explicit statement about providing open-source code or a link to a code repository. |
| Open Datasets | No | We evaluated the proposed estimator numerically on synthetic data in a setup similar to the experiments of (Oymak, 2019). ... B Rn p is generated randomly with i.i.d. standard normal entries. |
| Dataset Splits | No | The paper uses synthetic data and discusses generating 100 randomly generated instances of the problem for simulation, but does not describe any train/test/validation splits for a specific dataset. |
| Hardware Specification | No | The paper does not provide specific hardware details (e.g., CPU, GPU models) used for running the experiments. |
| Software Dependencies | No | For each choice of α and ρ, we solved (4) using Nesterov s Accelerated Gradient Method (AGM) (Nesterov, 1983; Nesterov, 2013, Section 2.2). The optimization task can be solved by the SGD as well. |
| Experiment Setup | Yes | In all of the experiments, we consider the dimensions to be n = 50, p = 100, and the time horizon to be T = 500. For α {0.2, 0.8} we choose A = αR with R being a uniformly distributed n n orthogonal matrix. Furthermore, B Rn p is generated randomly with i.i.d. standard normal entries. ... The nonlinearity in (1) is described by one of the functions... at ρ = 1 (i.e., linear activation), ρ = 0.5 (i.e., leaky Re LU activation with slope 0.5 over R 0), ρ = 0.3 (i.e., leaky Re LU activation with slope 0.3 over R 0), and ρ = 0 (i.e., Re LU activation). ... For the Gaussian model the step-size is set to 10 3, whereas for the heavy-tailed model the step-size is set to 10 4. In each trial, the AGM is run for a maximum of 500 iterations and terminated only if the relative error dropped below 10 8 (i.e., b C C 2 F/ C 2 F 10 8). |