Research map / Learning theory and algorithms / Sample complexity
On Empirical Risk Minimization with Dependent and Heavy-Tailed Data
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Huber loss instead of squared loss | ERM with sub-Gaussian inputs and Pareto noise · Stationary β-mixing linear regression | L2 estimation error rate: N^{-1/8} -> N^{-\frac{1}{2}+\iota} | Helped |
| Replace the small-ball condition with Lp-L2 norm-equivalence (p=8) (ablation) | Squared-loss ERM · Stationary exponentially β-mixing data | L2 estimation error rate: N^{-\frac{1}{4}+\iota} -> N^{-\frac{1}{2}+\iota} | Helped |
| Use a polynomial-tail interaction condition instead of the sub-Weibull interaction condition | Squared-loss ERM · Stationary exponentially β-mixing data | L2 estimation error rate: N^{-\frac{1}{4}+\iota} -> N^{-\frac{1}{4}\left(1-\frac{1}{\eta_2}\right)+\iota} | Hurt |
| Use a polynomial-tail interaction condition instead of the sub-Weibull interaction condition | ERM with locally strongly-convex loss · Stationary exponentially β-mixing data | L2 estimation error rate: N^{-\frac{1}{4}+\iota} -> N^{-\frac{(1-1/\eta_2)}{4}+\iota} | Hurt |
| Use Huber loss so the noise-input interaction is controlled through the clipped derivative | ERM with heavy-tailed noise and sub-Gaussian inputs · Stationary β-mixing linear regression | Confidence level of the risk bound: polynomial probability -> exponential probability | Helped |
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