Research map / Learning theory and algorithms / Matrix and tensor methods
Leveraged volume sampling for linear regression
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Rescale rows by inverse leverage scores and sample jointly with replacement | Volume sampling for linear regression · Worst-case linear regression | sample size for high-probability multiplicative loss bound: O(d^2/\epsilon) -> O(d\log d + d/\epsilon) | Helped |
| Use standard volume sampling rather than leveraged volume sampling | Linear regression · Worst-case linear regression | loss relative to optimum: 1 + \frac{n-k}{n-d} | Hurt |
| Use i.i.d. leverage score sampling rather than leveraged volume sampling | Linear regression · Small sample sizes | empirical performance | Hurt |
| Choose rescaling probabilities proportional to leverage scores | Rescaled volume sampling · Linear regression | expected covariance estimate: q_i=\frac{l_i}{d} | Helped |
| Use approximate rather than exact leverage scores for rescaling | Leveraged volume sampling · Large-scale linear regression | preprocessing runtime: O(nd^2) -> \widetilde{O}(nd + d^5) | Helped |
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