Timeline for Finding a function $\hat{\mu}:[0,1]\to\{0,1\}$ for a data set $X_i:[0,1]\to\{0,1\}$ that minimizes the sum of squared distances to that function
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 22 at 5:59 | answer | added | D.W.♦ | timeline score: 2 | |
| Oct 22 at 5:23 | comment | added | D.W.♦ | I understand your statement about the $L_p$ norm now, thank you for explaining. | |
| Oct 22 at 3:32 | comment | added | cgmil | @D.W. In general it's not true, but in this case it is. The integrand would be raised to the power $p$, but the integrand is only 0 or 1 at every $t$, so you're always computing $0^p$ or $1^p$ which does not depend on $p$ for $p > 1$. Second, if I assume finite discontinuities, then the function can be represented in a computer via just the points of discontinuity. That's what we will have in practice. | |
| Oct 21 at 21:17 | comment | added | D.W.♦ | How are the functions specified in the input (in finite length)? It takes infinitely many bits to specify a function on $[0,1]$. | |
| Oct 21 at 21:15 | comment | added | D.W.♦ | I don't think it's true that the $L_p$ norm is the $L_1$ norm raised to the power $1/p$. Are you sure about that statement? | |
| Oct 21 at 21:09 | history | asked | cgmil | CC BY-SA 4.0 |