Deep Learning: Difference between revisions
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<math>A(\epsilon) \geq 1 - (\frac{\pi}{8})^{1/2} \exp(-\frac{d-1}{2} \epsilon^2)</math> | <math>A(\epsilon) \geq 1 - (\frac{\pi}{8})^{1/2} \exp(-\frac{d-1}{2} \epsilon^2)</math> | ||
As d goes to infinity, the right hand side goes to 1. | As d goes to infinity, the right hand side goes to 1. | ||
In a high-dimensional space, an epsilon expansion will cover almost the entire area. | |||
;Theorem | ;Theorem | ||
c-class classification | c-class classification | ||
<math>\rho_c, u_c | <math>\rho_c, u_c</math> | ||
<math>f_c = \mu_1 \{x \mid | <math>v_c=\delta_{n-1} * u_c</math> is the max density relative to uniform density. | ||
<math>f_c = \mu_1 \{x \mid C(x)=c\}</math> is the area where the classifier <math>C</math> classifies as class c. | |||
Pick a class <math>f_c \leq \frac{1}{2}</math>. | Pick a class <math>f_c \leq \frac{1}{2}</math>. | ||
Sample x from <math>\rho_c</math>. | Sample x from <math>\rho_c</math>. | ||