-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 On 09/12/14 20:20, A. Johnson wrote: >> This indeed seems plausible under the powerful assumption that >> the underlying stat is constant. > > Actually it applies to any known relative pattern, for example, > that the number increases by 1 each time.
Still a very powerful assumption given the stats we're gathering. >> where the additive noise is applied to the center of the first >> bin? > > Yes, you can look at it like that. > >> I can see how this is better, since the underlying value gets >> immediately smoothed by binning. However, it does give me a weird >> hacky feeling... >> >> Is this construction something that has been used before? > > Well, the output here is a bin, not a number, and the “exponential > mechanism” is the generalization of the Laplace mechanism to > handle arbitrary output spaces > (kunaltalwar.org/papers/expmech.pdf). In this case, I believe that > adding Laplace noise to a bin center and then re-binning is a way > to select according to the distribution that the exponential > mechanism would prescribe. I see the value in switching algorithms and doing the binning step before adding noise. But I don't see the value of binning the result once more. In a sense, we're already binning signal + noise by cutting off the float part. I don't see what we gain by reducing resolution even more. It seems just unnecessary. Example: - We observe 123 things. - We round up to the next multiple of 8, so to 128. - We add Laplace noise -12.3456, obtain 110.6544, round down to 110. - Why would we round up to the next multiple of 8 again, to 112? It should be equally hard to infer the 128 value from 110 with bin size 1 or 112 with bin size 8. Unless I'm wrong. Please prove me wrong? :) For now, I'm going to switch algorithm order in the code and not add a second binning step. All the best, Karsten -----BEGIN PGP SIGNATURE----- Version: GnuPG v1 Comment: GPGTools - http://gpgtools.org iQEcBAEBAgAGBQJUiBUMAAoJEJd5OEYhk8hIw3MH/RIQWeN+MQalG/NWovKqiFiA /+FsEI/tGjzptnjPtYebHzrmor4xr1ZA3sdZA06MH887wypZY3+Gp47kTZYwIybD ytfqjHJa/nItgPORvjp4ILsvJ+7KIq563ovMxLz0ZsrLmlUARluO2Ri53HrIulEA attFlg98UzLht+UrYhOL/EdZXGVhOd3yuZg+PcFz1zxuYZZszH/6zjYu0oordVwG VnujgzSp9/7ggQahn/3grhpEbiNI6pDNi+pcGOu3VsbccCLn1gFJHglhK+HM70tx zhMwRzFRay+KFm7bgtXNPQkt7hvdckl9I3aSUQyx+Xwx5ylSCIgs4XK/QJ8xdNM= =NE+w -----END PGP SIGNATURE----- _______________________________________________ tor-dev mailing list [email protected] https://lists.torproject.org/cgi-bin/mailman/listinfo/tor-dev
