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Can samples be compressed?

No, the inequality is not guaranteed. One example with $k=2$ is for $g(x_1,x_2) = OR(x_1,x_2)$. Then $f_g(1;\theta) = 1-(1-\theta)^2$, and $\mathcal{I}_g(\theta) = 4/(2\theta-\theta^2)$. We have $\mat …
Yoav Kallus's user avatar
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