Timeline for Non asymptotic error bound for non parametric estamation $f(x)=\mathbb{E}[Y|X=x]$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
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| Apr 20, 2020 at 9:10 | comment | added | Aryeh Kontorovich | Look in Wainwright's high-dimensional statistics book. | |
| Apr 20, 2020 at 7:58 | comment | added | ess | @AryehKontorovich Any reference to the simpler setting? | |
| Apr 19, 2020 at 22:34 | comment | added | Aryeh Kontorovich | You can probably argue that the regressogram produces a Lipschitz (or maybe even Holder) smooth function, and then use covering numbers to derive generalization results. Our paper focuses on the computational aspects, in general doubling spaces, so it's probably an overkill for your needs. | |
| Apr 19, 2020 at 21:07 | comment | added | ess | @AryehKontorovich PS: I am not sure I understand what the paper does. I guess the result I am looking for is given by theorem 10 or corrolary 11. But the results are on $R_n(h,q)$, how do they transfer to $h$ (which is the equivalent of my $f$)? | |
| Apr 19, 2020 at 20:59 | comment | added | ess | @AryehKontorovich Thanks for you answer! Is there anything about the regressogram? I am surprised I cannot find anything in the literature (it is probably the simplest regression estimator), maybe I don't have the right keywords. | |
| Apr 19, 2020 at 20:56 | history | edited | ess | CC BY-SA 4.0 |
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| Apr 19, 2020 at 20:07 | comment | added | Aryeh Kontorovich | If you also assume $Y$ has bounded range (say, in $[0,1]$) then you can use covering numbers to give finite-sample bounds, as done, say, here: ieeexplore.ieee.org/document/7944658 | |
| Apr 19, 2020 at 15:27 | review | First posts | |||
| Apr 19, 2020 at 21:01 | |||||
| Apr 19, 2020 at 15:18 | history | asked | ess | CC BY-SA 4.0 |