pointcare inequality

[[concept]]

Topics

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Pointcare Inequality

Let $\mu$ be a probability measure on ${\mathbb{R}}^N$. We say that $\mu$ satisfies the Pointcare Inequality, denoted $PI(C)$, if for all differentiable $f$, ${\text{Var}}_{x\sim \mu }(f(x))\le C{\mathbb{E}}_{x\sim \mu }\left[||\nabla f|{|}^2\right]$

Notes

• ${\sum }_{i=1}^N{\mathbb{E}}_{}\left[({\partial }_{i}f(x){)}^2\right]$ is an expression of the function’s sensitivity to each coordinate
• Sometimes, $\nabla f$ is the “other” notion of "$\nabla$"

References

References

See Also

Mentions

Mentions

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