Fix maximize metrics.

[trivialfis]

Close #12612
Close #12621

notes

• ams is not a valid metric, a ratio is required.
• No test is added. Any test we add now is just manually copying the list to the test module.
• All language bindings.

Suggestion

We should deprecate these metrics and make all XGBoost metrics error-based metrics. For existing scores, we can use the inverse or minus.

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• R-package/R/callbacks.R

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Walkthrough

When maximize is unspecified, Python, R, and JVM metric-direction checks now recognize AMS and interval-regression accuracy as metrics to maximize. The R check also excludes names ending in _mape from its _map match.

Assessment against linked issues

Objective	Addressed	Explanation
Add ams@ and interval-regression-accuracy to Python early-stopping direction inference when maximize is unspecified [#12612]	✅

Out-of-scope changes

Code Change	Explanation
Add metric indicators to the R maximization rules (R-package/R/callbacks.R:691-696)	The linked objective specifies Python early stopping and does not state a requirement for the R callback.
Add metric indicators to the JVM maximization rules (jvm-packages/xgboost4j/src/main/java/ml/dmlc/xgboost4j/java/XGBoost.java:38)	The linked objective specifies Python early stopping and does not state a requirement for the JVM metric rules.

Priority: ➖ Normal

Severity of issue fixed: Medium

Merge Risk: ⚪ Minimal · up to d8e8b

The changed callbacks recognize AMS and interval-regression accuracy for automatic maximization, with no supported merge-blocking behavior remaining.

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