Research map / Learning theory and algorithms / Sample complexity
Linear regression without correspondence
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use row sampling and parameter-net enumeration | Unlabeled least-squares optimization · Worst-case inputs | approximation ratio: 1+\epsilon | Helped |
| Use lattice basis reduction on the structured Subset Sum instance | Unlabeled linear regression · Noiseless Gaussian covariates, appropriately quantized inputs | exact recovery probability: 1-\delta | Helped |
| Allow unknown correspondence instead of known covariate-response pairing | Linear regression · Gaussian covariates with Gaussian noise | SNR requirement for approximate recovery: d/\log\log(n); d/n | Hurt |
| Allow unknown correspondence instead of known covariate-response pairing | Linear regression · Uniform covariates on [-1/2,1/2]^d with Gaussian noise | SNR requirement for approximate recovery: C'; d/n | Hurt |
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