Research map / Learning theory and algorithms / Kernels and regression theory
On the number of variables to use in principal component regression
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use p = N instead of any p < n | PCR · Gaussian design with polynomial eigenvalue decay, noiseless | asymptotic prediction risk: limsup_N R_{κ}(1) / R_{κ}(α*) < 1 | Helped |
| Use a feature threshold ν = η1 rather than the best threshold in the ν > νb regime | PCR · Gaussian design with general eigenvalue decay, noiseless | asymptotic prediction risk: limsup_N R_f(η1,0) / R_f(ν*, 0) < 1 | Helped |
| Increase p through the interpolation threshold into the p > n regime | PCR · Gaussian design with polynomial eigenvalue decay, noiseless | asymptotic prediction risk: limsup_N R_{κ}(1) / R_{κ}(α*) < 1 | Mixed |
| Choose p in the p > n regime | PCR · Polynomial eigenvalue decay with κ < 1 | prediction risk | Helped |
| Choose p in the p > n regime | PCR · Polynomial eigenvalue decay with κ > 1 and positive noise | prediction risk | Hurt |
| Use p = o(n) rather than larger feature counts | PCR · Noisy setting where noise dominates model-misspecification error | asymptotic prediction risk | Helped |
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