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
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| Oct 22 at 20:01 | comment | added | D.W.♦ | @cgmil, Your argument assumes that the optimal function $\hat{\mu}$ has jump points at the same locations as the functions $f \in X$. I suspect that isn't necessarily true and it is possible to reduce the value of the objective function by choosing a function $\hat{\mu}$ that has additional jump points, such as in my answer above. Such a function $\hat{\mu}$ won't correspond to any solution to the discrete problem (it can't be translated back to a solution to the discrete version of the problem). | |
| Oct 22 at 15:37 | comment | added | cgmil | That does make sense. Now, on to my suspicion that it might be intractable due to relating it to the discrete problem. What's my error? (Reasoning about algorithm complexity is not something I've ever been trained to do, so I'd like to know what error I may have made.) | |
| Oct 22 at 5:59 | history | answered | D.W.♦ | CC BY-SA 4.0 |