Exponential Reduction in Sample Complexity with Learning of Ising Model Dynamics
Authors: Arkopal Dutt, Andrey Lokhov, Marc D Vuffray, Sidhant Misra
ICML 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We quantify through a carefully designed set of experiments and a rigorous mathematical analysis the reduction in sample complexity that one can achieve using samples from Glauber dynamics. We perform an extensive set of numerical experiments to empirically obtain m for a variety of graphs in both the T-regime and the M-regime. Our sample complexity results for the T-regime and Mregime are shown in Figure 1a and Figure 1b respectively. |
| Researcher Affiliation | Academia | 1Massachusetts Institute of Technology, Cambridge, MA, USA 2Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM, USA. |
| Pseudocode | Yes | Algorithm 1 Active Learning of Glauber Dynamics |
| Open Source Code | Yes | The code for the learning algorithms, active learner and data in this work is available on Git Hub1. 1https://github.com/lanl-ansi/ learning-ising-dynamics |
| Open Datasets | Yes | We consider the dataset from (Prentice et al., 2016) containing spike trains from 152 salamander retinal ganglion cells in response to a non-repeated natural movie stimulus, of which we select spike trains over n = 42 neurons over 24s for our application. |
| Dataset Splits | No | The paper specifies a protocol to find the minimal number of samples required for successful reconstruction with a certain confidence level ('successively reconstruct the structure 45 times in a row from 45 independent sets of m samples, which guarantees a 90% confidence for δ = 0.05'), but it does not describe traditional training, validation, or test dataset splits in terms of percentages or counts for different data partitions. |
| Hardware Specification | No | The paper does not provide any specific details about the hardware used for running the experiments. |
| Software Dependencies | No | The paper does not mention any specific software names with version numbers that would allow for reproducible setup of dependencies. |
| Experiment Setup | Yes | In deciding the ℓ1-regularization to be used, optimal values of cλ which are unknown apriori were determined through detailed numerical simulations on different Ising model topologies as described in Appendix S3. The determined optimal values of cλ are summarized in Table 1 on lattices and random regular (RR) graphs for the two different regimes. |