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].
Identifiability and Asymptotics in Learning Homogeneous Linear ODE Systems from Discrete Observations
Authors: Yuanyuan Wang, Wei Huang, Mingming Gong, Xi Geng, Tongliang Liu, Kun Zhang, Dacheng Tao
JMLR 2024 | Venue PDF | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We also construct simulations with various system dimensions to illustrate the established theoretical results. Keywords: identifiability, linear ODEs, asymptotic analysis, nonlinear least squares, causal discovery. 4. Simulations In this section, we illustrate the theoretical results established in Section 3 by simulation. |
| Researcher Affiliation | Academia | School of Mathematics and Statistics University of Melbourne, Melbourne, Australia; School of Computer Science, Faculty of Engineering The University of Sydney, Sydney, Australia; Carnegie Mellon University, Pittsburgh, PA, USA; Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, UAE |
| Pseudocode | No | The paper does not contain any structured pseudocode or algorithm blocks. |
| Open Source Code | No | The paper does not explicitly state that source code for the methodology is provided or publicly available. |
| Open Datasets | No | For each d = 2, 3, 4, we first randomly generate a d d parameter matrix A d and a d 1 initial condition x 0d as the true system parameters for each d-dimensional ODE system (1). This indicates the data was simulated, not obtained from an open dataset. |
| Dataset Splits | No | Then n equally-spaced noisy observations are generated based on Equation (4) in [0, 1] time interval with error term ϵi N(0, diag(0.052, . . . , 0.052)). We tested various sample sizes for each d-dimensional ODE system. For each configuration, we run 200 random replications. The paper simulates data for each experiment run and does not use pre-defined training/test/validation splits from a larger fixed dataset. |
| Hardware Specification | No | The paper does not provide specific hardware details used for running its experiments. |
| Software Dependencies | No | The paper mentions using a 'bound-constrained minimization technique (Branch et al., 1999)' but does not specify any software names with version numbers for implementation. |
| Experiment Setup | Yes | For each d = 2, 3, 4, we first randomly generate a d d parameter matrix A d and a d 1 initial condition x 0d as the true system parameters for each d-dimensional ODE system (1). Without loss of generality, we set T = 1. Then n equally-spaced noisy observations are generated based on Equation (4) in [0, 1] time interval with error term ϵi N(0, diag(0.052, . . . , 0.052)). We tested various sample sizes for each d-dimensional ODE system. For each configuration, we run 200 random replications. Firstly, we initialize the parameter with a value close to the true parameter (for example, θ ± 0.001). Secondly, we constrain the bounds of the parameter within a reasonable neighbourhood of the true parameter (for example, [θ − 0.5, θ + 0.5]). |