[shivamkumxr]

Reference Issues/PRs

Closes #3948

What does this implement/fix? Explain your changes.

Adds PELTSegmenter under aeon.segmentation based on Killick et al. (2012).

Summary of changes:

• Implemented PELTSegmenter on top of BaseSegmenter.
• Uses prefix sums to compute segment costs in $O(1)$ time with NumPy.
• Added pruning step to discard candidate changepoints as the series is traversed.
• Supported costs: L2 (mean shifts) and Gaussian log-likelihood (mean + variance shifts).
• Penalty can be passed directly as a float or chosen via 'bic' / 'aic'.
• Works on multivariate series by computing costs across channels.
• Added tests in test_pelt.py and patched _yield_segmentation_checks.py to handle empty changepoint edge cases during generic estimator checks.

Does your contribution introduce a new dependency? If yes, which one?

No.

PR checklist

• The PR title starts with [ENH].
• Added PELTSegmenter to API documentation (docs/api_reference/segmentation.rst).
• Added unit tests (test_pelt.py) and docstrings following numpydoc standards.
• Verified compatibility with check_estimator(PELTSegmenter).

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• Run numba-disabled codecov tests
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• Regenerate expected results for testing
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[baraline]

Not a correctness review, only looked at testing side, some functions to move.