Research map / Learning theory and algorithms / Sample complexity
$k$-Sliced Mutual Information: A Quantitative Study of Scalability with Dimension
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use 1-SMI instead of classic MI | Independence testing with a one-dimensional shared sinusoidal feature · Synthetic independence testing | AUC ROC | Helped |
| Use 2-SMI to match the rank-2 shared signal | Independence testing · Synthetic rank-2 common signal | AUC ROC | Helped |
| Use 3-SMI instead of 2-SMI for a rank-3 shared signal | Independence testing · Synthetic rank-3 common signal | AUC ROC | Helped |
| Use sliced MI with k below the ambient dimension instead of classic MI | Independence testing · Synthetic high-dimensional dependence tests | AUC ROC | Helped |
| Increase projection dimension to match the intrinsic dimension of the shared signal | k-SMI independence testing · Synthetic shared-signal models | AUC ROC | Mixed |
| Replace the single shared neural estimator with parallel neural estimators over projections | k-SMI neural estimator · Gaussian X = Y = N(0, I_d) | Convergence rate | Helped |
| Replace classic MI with 1-SMI | InfoGAN · MNIST | Latent-factor disentanglement | No clear effect |
| Replace classic MI with 5-SMI | InfoGAN · MNIST | Latent-factor disentanglement | No clear effect |
| Increase ambient dimension under identity marginal covariance and sublinear growth of Fisher information | Monte Carlo k-SMI estimator · High-dimensional estimation | Monte Carlo error bound: O(sqrt(k(1/d_x+1/d_y)/m)) | Helped |
| Use projection-based neural estimation instead of classic-MI smoothness requirements | k-SMI neural estimator · Neural estimation over F^k_{d_x,d_y}(M,b) | Required density smoothness: ⌊(d_x +d_y)/2 ⌋+3 -> k+3 | Helped |
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