Research map / Learning theory and algorithms / Sample complexity
Ising Model Selection Using $\ell_{1}$-Regularized Linear Regression: A Statistical Mechanics Analysis
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ℓ1-regularized linear regression for neighborhood selection | Ising model selection on typical paramagnetic random regular graphs · Typical paramagnetic random regular graphs | sample complexity: M >\frac{c\left(\lambda,K_{0}\right)\log N}{\lambda^{2}} | Helped |
| Use ℓ1-LinR rather than a model-matched logistic estimator | Ising model selection · Typical paramagnetic random regular graphs | sample complexity order: M=\mathcal{O}\left(\log N\right) | No clear effect |
| Use ℓ1-LinR with regularization parameter outside the range 0<λ<tanh(K₀) | ℓ1-LinR · Typical paramagnetic random regular graphs | recall | Hurt |
| Replace the active-set expectation with a finite-sample average in the reduced estimator | ℓ1-LinR non-asymptotic prediction · Moderate M,N | prediction of precision | Helped |
| Apply the typical tree-like analysis to a loopy 2D grid | ℓ1-LinR theoretical predictions · 15 × 15 2D grid | agreement between theoretical and numerical results | Helped |
| Increase the constant c above the predicted critical value c₀ | ℓ1-LinR with M=c log N and λ=0.3 · Typical random regular graphs as N increases | precision | Helped |
| Set the constant c below the predicted critical value c₀ | ℓ1-LinR with M=c log N and λ=0.3 · Typical random regular graphs as N increases | precision | Hurt |
| Use ℓ1-LogR instead of ℓ1-LinR | Ising model selection · Random regular graph experiments | residual sum of squares | Helped |
Closest papers by meaning
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