Research map / Learning theory and algorithms / Matrix and tensor methods
High-Dimensional Optimization in Adaptive Random Subspaces
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an adaptive Gaussian sketch instead of an oblivious Gaussian sketch at m=256 | Logistic regression with random Fourier features · MNIST test, λ=5 · 10⁻⁶ | test classification error: 30.1% -> 2.8% | Helped |
| Use an adaptive Gaussian sketch instead of Nystrom at m=256 | Logistic regression with random Fourier features · MNIST test, λ=5 · 10⁻⁶ | test classification error: 3.0% -> 2.8% | Helped |
| Use an adaptive Gaussian sketch instead of an oblivious Gaussian sketch at m=1024 | Logistic regression with random Fourier features · CIFAR10 test, λ=5 · 10⁻⁶ | test classification error: 80.1% -> 45.8% | Helped |
| Use an adaptive Gaussian sketch instead of Nystrom at m=1024 | Logistic regression with random Fourier features · CIFAR10 test, λ=5 · 10⁻⁶ | test classification error: 55.8% -> 45.8% | Helped |
| Increase sketch dimension from 64 to 256 (ablation) | Adaptive Gaussian sketch · MNIST test, λ=10⁻⁵ | test classification error: 8.1 -> 2.4 | Helped |
| Increase sketch dimension from 256 to 1024 (ablation) | Adaptive Gaussian sketch · CIFAR10 test, λ=10⁻⁵ | test classification error: 47.7 -> 46.2 | Helped |
| Apply iterative refinement using the same sketch across iterations (ablation) | Adaptive sketching · MNIST even-vs-odd classification | relative solution error | Helped |
| Use the power method with q=2 to form the sketch (ablation) | Iterative adaptive sketching · MNIST even-vs-odd classification | relative solution error | Helped |
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