Learning Low-dimensional Latent Dynamics from High-dimensional Observations: Non-asymptotics and Lower Bounds
Authors: Yuyang Zhang, Shahriar Talebi, Na Li
ICML 2024 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We simulate our algorithm for a set of simple systems where r = m = 1, Σw = 0 and ση = 1. We use A = 0.9, B = 1 and randomly sample C with orthonormal columns. We choose inputs with covariance Σu = 0.1. The choice of n will be clear in the context. The results are reported in Figure 1. |
| Researcher Affiliation | Academia | Yuyang Zhang 1 Shahriar Talebi 1 Na Li 1 1SEAS, Harvard University, Cambridge, USA. |
| Pseudocode | Yes | Algorithm 1 Column Space Projection SYSID (Col-SYSID) Algorithm 2 Column Space Approximation (Col-Approx) Algorithm 3 Meta Column Space Projection SYSID (Meta-Col-SYSID) Algorithm 4 Ho-Kalman |
| Open Source Code | No | The paper does not contain any statements about making its source code publicly available, nor does it provide a link to a code repository. |
| Open Datasets | No | The paper uses simulated data for its experiments, stating, 'We simulate our algorithm for a set of simple systems where r = m = 1, Σw = 0 and ση = 1.' It does not refer to any pre-existing public datasets with access information. |
| Dataset Splits | Yes | We consider system M and datasets D1 = U1 Y1, D2 = U2 Y2 (with lengths T1, T2 respectively) in HDSYSID. ... If T1 κ3 n2r3, T2 κ1 poly (r, m)... |
| Hardware Specification | No | The paper does not provide any specific details about the hardware (e.g., CPU, GPU models, memory, or cluster specifications) used to run the experiments. |
| Software Dependencies | No | The paper does not list any specific software dependencies, libraries, or solvers with version numbers. |
| Experiment Setup | Yes | We simulate our algorithm for a set of simple systems where r = m = 1, Σw = 0 and ση = 1. We use A = 0.9, B = 1 and randomly sample C with orthonormal columns. We choose inputs with covariance Σu = 0.1. ... We first simulate Col-Approx (Algorithm 2) with n = 40, 80, 160, 320 and a single trajectory data of length T = 10000 separately (Figure 1.Left). Next, we simulate Col-SYSID (Algorithm 1) with T = 10000 and n = 320 (Figure 1.Center). |