Research map / Learning theory and algorithms / Sample complexity
List-decodable Linear Regression
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use certifiably anti-concentrated inliers and SoS pseudo-distributions with rounding by votes | List-decodable linear regression · List-decodable linear regression | list size: O(1/α) | Helped |
| Use certifiably anti-concentrated Gaussian inliers with bounded covariance condition number | List-Decodable Regression · Gaussian inliers | runtime: (d/αη)^{O(1/(α^8η^8))} | Helped |
| Restrict the target to equal-magnitude Boolean coordinates and use anti-concentration only in Boolean directions | List-Decodable Regression · Product-distribution inliers | sample complexity: (d/αη)^{O(1/(α^2η^2))} | Helped |
| Assume only ordinary anti-concentration for a general distribution rather than a certifiable condition | List-decodable regression · General inlier distributions | algorithmic efficiency | Hurt |
| Use inliers that fail the required anti-concentration condition | List-decodable regression · [q]^d inliers | minimum list size for the stated approximation guarantee: list of size < d | Hurt |
| Allow independent additive label noise with variance ζ² and modify the constraints and selected subset size | List-Decodable Regression · Noisy inlier labels | parameter error: ζ/α + η | Hurt |
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