File:Visual proof of the optimality of the Probability Jaccard Index on Three element distributions.png
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Summary
| Description |
English: The probability jaccard index is optimal in the following sense. If a sampling method has more collisions than the probability jaccard index on two distributions, x and y, then there must be a pair of distributions that are more similar under the probability jaccard index than x and y are on which that sampling method has fewer collisions.
This diagram shows the proof mechanism graphically on 3 element distributions. For x and y to collide more on the green element, they have to give up collisions with z on either red or blue, and can’t gain any more on green to compensate. As a result, the collisions with z must decrease, but z is more similar to both x and y than they are to each other. |
| Date | |
| Source | Own work |
| Author | Ryan Moulton |
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| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 18:38, 7 February 2020 | | 1,140 × 671 (68 KB) | Moultano | User created page with UploadWizard |
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