Timeline for Does there exist a Penalized Conditional Expectation?
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 1, 2016 at 22:29 | vote | accept | ABIM | ||
| Oct 1, 2016 at 15:10 | comment | added | ABIM | Are there any relating to stochastic processes? | |
| Oct 1, 2016 at 6:00 | comment | added | R Hahn | You may already know this, but "penalized likelihood methods" or "penalized empirical risk minimization" in statistics are based on this type of equation. Keywords would include "ridge regression" or Tikhonov regularization as well as the lasso estimator. There are huge bodies of literature on these topics. | |
| Oct 1, 2016 at 4:06 | answer | added | usul | timeline score: 3 | |
| Oct 1, 2016 at 3:36 | comment | added | ABIM | Yes this sounds very promising, references would be very much appreciated. I worked out a proof sketch and I also noticed it must be a conditional expectation, so that's good. Please do send the references. Thanks | |
| Oct 1, 2016 at 0:21 | comment | added | usul | This is a bit different, but we know a fair amount about $\mathbb{E} L(Z,Y)$ for other loss functions $L$. If $L$ is any Bregman divergence, then the solution is still the conditional expectation. For example of other cases, if $L(Z,Y) = |Z-Y|$ then the solution is the median, and so on. If this approach interests you I can try to give references. | |
| Sep 29, 2016 at 11:33 | comment | added | SBF | I mean something of the kind "for $\lambda$ small enough, the optimal solution is $F = \Bbb E[Z|Y] + ...$" | |
| Sep 29, 2016 at 2:06 | comment | added | ABIM | What do you mean by local deviation? | |
| Sep 28, 2016 at 8:55 | comment | added | SBF | I would not expect as elegant results in the penalized case: the original minimization problem (with $\lambda = 0$) is quadratic, optimizer is linear and can be nicely characterized as a projection of $Z$ onto $\sigma(Y)$. I'd expect you can get some local deviation results for $\lambda \ll 1$, however not sure whether you'd find them useful. | |
| Sep 27, 2016 at 23:24 | history | edited | Gerry Myerson | CC BY-SA 3.0 |
typo in title
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| Sep 27, 2016 at 18:20 | history | asked | ABIM | CC BY-SA 3.0 |