For Gaussian mean estimation and linear regression with distribution shift, the paper claims that public data never provides complementary value: either public data alone suffices, or (for large shifts) private data alone must solve the problem.
The power of the hybrid model for mean estimation
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Lower Bounds for Public-Private Learning under Distribution Shift
For Gaussian mean estimation and linear regression with distribution shift, the paper claims that public data never provides complementary value: either public data alone suffices, or (for large shifts) private data alone must solve the problem.