Interaction Screening: Efficient and Sample-Optimal Learning of Ising Models
Authors: Marc Vuffray, Sidhant Misra, Andrey Lokhov, Michael Chertkov
NeurIPS 2016 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | Section 4 illustrates performance of our reconstruction algorithm via simulations. Here we show on a number of test cases that the sample complexity of the suggested method scales logarithmically with the number of variables and exponentially with the maximum coupling intensity. and We test performance of the Struct-RISE, with the strength of the l1-regularization parametrized by 1 n ln(3p2/ϵ), on Ising models over two-dimensional grid with periodic boundary conditions (thus degree of every node in the graph is 4). We have observed that this topology is one of the hardest for the reconstruction problem. We are interested to find the minimal number of samples, nmin, such that the graph is perfectly reconstructed with probability 1 ϵ 0.95. In our numerical experiments, we recover the value of nmin as the minimal n for which Struct-RISE outputs the perfect structure 45 times from 45 different trials with n samples, thus guaranteeing that the probability of perfect reconstruction is greater than 0.95 with a statistical confidence of at least 90%. |
| Researcher Affiliation | Academia | Marc Vuffray1, Sidhant Misra2, Andrey Y. Lokhov1,3, and Michael Chertkov1,3,4 1Theoretical Division T-4, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 2Theoretical Division T-5, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 3Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM 87545, USA 4Skolkovo Institute of Science and Technology, 143026 Moscow, Russia |
| Pseudocode | No | The paper describes the steps of the algorithm but does not include a clearly labeled pseudocode block or algorithm figure. |
| Open Source Code | No | The paper does not contain an explicit statement about releasing code or a link to a source code repository for the methodology described. |
| Open Datasets | No | The paper describes generating samples from Ising models ("samples generated by Glauber dynamics", "sample directly from the exhaustive weighted list of the 216 possible spin configurations") but does not refer to a specific publicly available dataset with concrete access information (link, DOI, repository, or formal citation). |
| Dataset Splits | No | The paper describes simulating data for evaluation ("samples generated by Glauber dynamics", "sample directly from the exhaustive weighted list of the 216 possible spin configurations") and determining the minimum number of samples for perfect reconstruction, but it does not specify explicit training, validation, or test dataset splits (e.g., percentages or counts) or refer to standard predefined splits for reproducibility. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used for running the experiments (e.g., exact CPU/GPU models, memory specifications). |
| Software Dependencies | No | The paper does not provide specific version numbers for any software dependencies, libraries, or solvers used in the experiments. |
| Experiment Setup | Yes | We test performance of the Struct-RISE, with the strength of the l1-regularization parametrized by 1 n ln(3p2/ϵ), on Ising models over two-dimensional grid with periodic boundary conditions (thus degree of every node in the graph is 4). and The couplings are chosen uniform and positive θ ij = 0.7. and The structure is recovered by thresholding the reconstructed couplings at the value α/2 = β/2. |