Research map / Learning theory and algorithms / Sample complexity
Robust Testing in High-Dimensional Sparse Models
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Require robustness to an ε-fraction of arbitrary corruptions | Sparse Gaussian mean testing with ℓ0 sparsity · Sparse Gaussian mean testing | sample complexity: non-robust: \Theta(\frac{s}{\gamma^2}\log(1+\frac{d}{s^2})) if s<\sqrt{d}; \Theta(\frac{\sqrt{d}}{\gamma^2}) if s\ge \sq | Mixed |
| Require robustness to an ε-fraction of arbitrary corruptions | Sparse Gaussian mean testing with ℓq sparsity · Sparse Gaussian mean testing | sample complexity: non-robust: \Theta(\frac{m}{\gamma^2}\log(1+\frac{d}{m^2})) if m<\sqrt{d}; \Theta(\frac{\sqrt{d}}{\gamma^2}) if m\ge \sq | Mixed |
| Require robustness to an ε-fraction of arbitrary corruptions | Sparse linear regression testing · Sparse linear regression | sample complexity: non-robust: Θ(min(\frac{s}{\gamma^2}\log(1+\frac{d}{s^2}),\frac{1}{\gamma^4})) if s<\sqrt{d}; Θ(min(\frac{\sqrt{d}}{\gam | Mixed |
| Use robust sparse mean estimation followed by testing for ℓq-constrained means | Robust sparse Gaussian mean testing · Sparse Gaussian mean testing, ℓq sparsity | sample complexity upper bound: n = \bigO{\frac{1}{\eps^2}\mleft(m\log\frac{d}{\eps}+\log\frac{1}{\delta}\mright)} | Helped |
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