Ising Model Selection Using $\ell_{1}$-Regularized Linear Regression: A Statistical Mechanics Analysis
Authors: Xiangming Meng, Tomoyuki Obuchi, Yoshiyuki Kabashima
NeurIPS 2021 | Conference PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We theoretically analyze the typical learning performance of ℓ1-regularized linear regression (ℓ1-Lin R) for Ising model selection using the replica method from statistical mechanics. For typical random regular graphs in the paramagnetic phase, an accurate estimate of the typical sample complexity of ℓ1-Lin R is obtained. Remarkably, despite the model misspecification, ℓ1-Lin R is model selection consistent with the same order of sample complexity as ℓ1-regularized logistic regression (ℓ1-Log R), i.e., M = O (log N), where N is the number of variables of the Ising model. Moreover, we provide an efficient method to accurately predict the nonasymptotic behavior of ℓ1-Lin R for moderate M, N, such as precision and recall. Simulations show a fairly good agreement between theoretical predictions and experimental results, even for graphs with many loops, which supports our findings. |
| Researcher Affiliation | Academia | Xiangming Meng Institute for Physics of Intelligence The University of Tokyo 7-3-1, Hongo, Tokyo 113-0033, Japan meng@g.ecc.u-tokyo.ac.jp; Tomoyuki Obuchi Department of Systems Science Kyoto University Kyoto 606-8501, Japan obuchi@i.kyoto-u.ac.jp; Yoshiyuki Kabashima Institute for Physics of Intelligence The University of Tokyo 7-3-1, Hongo, Tokyo 113-0033, Japan kaba@phys.s.u-tokyo.ac.jp |
| Pseudocode | Yes | Algorithm 1: Method to solve EOS (19) together with (25) |
| Open Source Code | No | The paper mentions in its self-assessment |
| Open Datasets | No | The paper describes generating its own data for experiments: |
| Dataset Splits | No | The paper does not specify explicit training, validation, and test splits for the data generated or used in its experiments. |
| Hardware Specification | No | The paper does not provide specific details about the hardware used to run the experiments, such as GPU models or CPU specifications. In its self-assessment, it indicates 'N/A' for computing resources. |
| Software Dependencies | No | The paper does not list specific software dependencies with version numbers. |
| Experiment Setup | Yes | The RR graph G GN,d,K0 with node degree d = 3 and coupling strength K0 = 0.4 is considered... The active couplings {Jij}(i,j) E have the same probability of taking both signs of +1 or 1/2... To obtain standard error bars, we repeat the sequence of operations 1000 times... Fig. 2 shows... for N = 200 with different values of α M/N... a 15 x 15 2D grid with uniform constant coupling K0 = 0.2... When λ = 0.3... |