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szcf-weiya / ESL-CN

The Elements of Statistical Learning (ESL)的中文翻译、代码实现及其习题解答。
https://esl.hohoweiya.xyz
GNU General Public License v3.0
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这是怎么计算得来的 #193

Closed duniang818 closed 5 years ago

duniang818 commented 5 years ago

Since this corresponds to a fraction r of the unit volume, the expected edge length will be e p (r) = r 1/p . In ten dimensions e 10 (0.01) = 0.63 and e 10 (0.1) = 0.80,

szcf-weiya commented 5 years ago

The volume of a $p$-dimensional hypercube is $$ V = c_p r^p $$ where $c_p$ is a constant. Then for the unit hypercube, the volume is $c_p$, and hence the fraction is $r^p$. So ...