DOC Improve plot_precision_recall

[lucyleeow]

Reference Issues/PRs

closes #18719

What does this implement/fix? Explain your changes.

• Avoid using the term 'false positive rate' as this is a technical term meaning FP/FP+TN, which is not accurate here. (False discovery rate would be more accurate as it is FP/FP+TP but I've avoided use of either term). Also avoided use of 'false negative rate' even though this is not a technical term.
• Avoid focusing on 'number' of results returned, as technically proportion of relevant results returned is more relevant
• Moves precision/recall definitions up.
• Removes F1 definition, we only mention it once and never talk about it again and it does not tie in to any other part of the example

Any other comments?

Happy to change wording.

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[ogrisel]

Thanks for the PR. Here is a quick suggestion but otherwise LGTM!

[ogrisel]

I think we can avoid introducing the word "relevancy" and more directly state:

Suggested change

	measure of result relevancy, while recall is a measure of how many of the
	relevant results are returned. 'Relevancy' here refers to items that are
	postively labeled, true positives and false negatives.
	measure of the fraction of relevant items among actually returned items while recall
	is a measure of the fraction of items that were returned among all items that should
	have been returned.

[lucyleeow]

Thanks!

[ArturoAmorQ]

Thanks for addressing this issue @lucyleeow. Here is just a nit but otherwise LGTM.

[ArturoAmorQ]

I think "fewer" is more gramatically correct in this context than "low" false positives/negatives. What do you think of a phrasing:

High precision corresponds to fewer false positives in returned results, and high recall corresponds to fewer false negatives in relevant results.

I also feel that the word "relates" is a bit vague. We can alternatively say something similar to:

High precision can be achieved by having few false positives in the returned results, and high recall can achieved by having few false negatives in the relevant results.