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[ENH] Implement AutoPlait segmenter #3067

@MatthewMiddlehurst

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@MatthewMiddlehurst

Describe the feature or idea you want to propose

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)

(from #2765)

Describe your proposed solution

Implement the algorithm in our segmentation module.

Describe alternatives you've considered, if relevant

No response

Additional context

See #2765 and #3044 for previous PRs. These may be useful but are incomplete. Do not feel like you have to reuse any of the code here.

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    enhancementNew feature, improvement request or other non-bug code enhancementimplementing algorithmsImplementing new algorithms/estimatorssegmentationSegmentation package

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