[ENH] Added AutoPlait segmentation algorithm.

[danielroberts20]

What does this implement/fix? Explain your changes.

Added Segmenter implementation for AutoPlait time series segmentation algorithm [1]. AutoPlait models a time series using Hidden Markov Models to determine when to stay or switch between different models (known as regimes). Time ticks at which it is cost-effective (according to Minimum Description Length) to switch between regimes are identified as change points of segments. AutoPlait is also able to identify common patterns in a time series.

[1] Yasuko Matsubara, Yasushi Sakurai, and Christos Faloutsos. "AutoPlait: Automatic Mining of Co-evolving Time Sequences." SIGMOD 2014. (DOI)

Any other comments?

This algorithm forms part of university dissertation that is in it's final days before submission. As such, some areas of the code are not as polished/Pythonic as I would like them to be. Any suggestions for changes are welcome.

PR checklist

For all contributions

• I've added myself to the list of contributors. Alternatively, you can use the @all-contributors bot to do this for you after the PR has been merged.
• The PR title starts with either [ENH], [MNT], [DOC], [BUG], [REF], [DEP] or [GOV] indicating whether the PR topic is related to enhancement, maintenance, documentation, bugs, refactoring, deprecation or governance.

For new estimators and functions

• I've added the estimator/function to the online API documentation.

[aeon-actions-bot]

Thank you for contributing to aeon

I have added the following labels to this PR based on the title: [ $\color{#FEF1BE}{\textsf{enhancement}}$ ].
I have added the following labels to this PR based on the changes made: [ $\color{#0e8a16}{\textsf{segmentation}}$ ]. Feel free to change these if they do not properly represent the PR.

The Checks tab will show the status of our automated tests. You can click on individual test runs in the tab or "Details" in the panel below to see more information if there is a failure.

If our pre-commit code quality check fails, any trivial fixes will automatically be pushed to your PR unless it is a draft.

Don't hesitate to ask questions on the aeon Slack channel if you have any.

PR CI actions

These checkboxes will add labels to enable/disable CI functionality for this PR. This may not take effect immediately, and a new commit may be required to run the new configuration.

• Run pre-commit checks for all files
• Run mypy typecheck tests
• Run all pytest tests and configurations
• Run all notebook example tests
• Run numba-disabled codecov tests
• Stop automatic pre-commit fixes (always disabled for drafts)
• Disable numba cache loading
• Push an empty commit to re-run CI checks

[MatthewMiddlehurst]

Thanks. Seems to be a couple of errors currently. Any chance you have some results which show this is comparable in performance to the original?