Research map / Learning theory and algorithms / Matrix and tensor methods
Outlier-robust estimation of a sparse linear model using $\ell_1$-penalized Huber's $M$-estimator
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ℓ1-penalized Huber loss for sparse regression with adversarially contaminated labels | Sparse linear regression with Gaussian design · Gaussian design with adversarial label outliers | estimation error rate: \sigma\Big(\frac{s\log (p/s)}{n}\Big)^{1/2} + \frac{\sigma o}{n} versus \sigma\Big(\frac{s\log p}{n}\Big)^{1/2} + \sigma | Helped |
| Apply ℓ1-penalized Huber estimation to the synthetic contaminated-label setting | ℓ1-penalized Huber's M-estimator · Synthetic experiment (n=1000, p=100; s=5,15,25) | square-root mean squared error | Mixed |
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