Timeline for Why does the L2 norm heuristic work in measuring uniformity of probability distributions?
Current License: CC BY-SA 3.0
6 events
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| Oct 7, 2021 at 11:28 | comment | added | Arbuja | @Whuber I'm not sure if that's always the case. In statistics, the Chi-Square distribution is most important but according to this post the LP norms still have importance. | |
| Dec 3, 2016 at 12:02 | comment | added | Ketan | Agree, Chi-squared being the formal way is undoubtedly the most reliable, but like I've said, in practical applications the slightly lower variation in values using this heuristic (without scaling) has been useful, at least in my particular application. | |
| Dec 2, 2016 at 16:05 | comment | added | whuber♦ | Ketan, (1) The chi-squared statistic has a global minimum at 0, which is more natural than 1/2. (2) Because the chi-squared statistic can be directly related to a formal hypothesis test of uniformity, it is far more useful and informative than the $L_2$ norm. (3) None of the properties you have yet identified for the $L_2$ norm distinguish it from any other $L_p$ norm for $p\gt 1$ (or from many other mathematical functions one might devise, for that matter). (4) The chi-squared statistic properly accounts for sample size, which the $L_2$ norm does not. | |
| Dec 2, 2016 at 7:37 | comment | added | Ketan | Using the chi-squared statistic is definitely more theoretically current, but I've found that in practical application, the norm heuristic works relatively better without scaling, and feels to be more performant. Moreover, the fact that it innately has this convex shape and a global minimum at 0.5 for all variable coordinates, is in itself a valid and relevant property to leverage, independent of the fact that it's similar to the chi-squared statistic. | |
| Dec 1, 2016 at 9:26 | vote | accept | Ketan | ||
| Nov 30, 2016 at 17:41 | history | answered | whuber♦ | CC BY-SA 3.0 |