Research map / Learning theory and algorithms / Kernels and regression theory
Generalization Properties of Learning with Random Features
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use random features count of order sqrt(n) log n instead of n in ridge regression with random features | RF ridge regression with lambda = n^-1/2 · statistical learning, least squares (worst case) | learning error (excess risk) rate | No clear effect |
| Use problem-dependent (compatibility-based, leverage-like) sampling of random features instead of uniform sampling | RF ridge regression fast rates · statistical learning, fast rates | number of random features required | Helped |
| Increase smoothness/regularity assumption r and reduce RKHS size gamma for fast rates with uniform sampling | RF ridge regression with uniform sampling · statistical learning, fast rates | number of random features required for optimal rate | Helped |
| Faster learning rates (r>1/2) with uniform sampling require more features in some regimes | RF ridge regression with uniform sampling · statistical learning, fast rates | number of random features required | Hurt |
| Empirical validation of predicted scaling of lambda, M and excess risk on spline kernel synthetic data | RF-KRR · synthetic spline kernel, n from 1000 to 10000 | agreement of predicted vs measured rates | No clear effect |
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