[ENH] Multioutput capability for all time series classifiers and regressors, broadcasting and tag

[Vasudeva-bit]

Reference Issues/PRs

Related to #5182, #5286

Depends on #5651, which should be merged first.

What does this implement/fix? Explain your changes.

Adds broadcasting support to let classifiers and regressors handle multioutput data.

What should a reviewer concentrate their feedback on?

Kindly give feedback on whether I am going in right direction.

PR checklist

For all contributions

• The PR title starts with either [ENH], [MNT], [DOC], or [BUG]. [BUG] - bugfix, [MNT] - CI, test framework, [ENH] - adding or improving code, [DOC] - writing or improving documentation or docstrings.

[Vasudeva-bit]

It has been a while since I last worked on this issue, I would like to get a quick clarification before starting again.
Kindly help me know which of the below methods is better:

1. As discussed here i.e., extend required classifiers and regressors for multioutput y.

I suppose setting false as a default has only be done in the base class.

Only classes need to be adapted that support multitarget prediction natively.

2. Otherwise, modify only classification and regression base classes similar to sktime/transformations/base.py i.e., base class handles multioutput based on the tag "capability:multioutput" assigned in estimator (classifier/regressor) classes.
   @fkiraly

[fkiraly]

Yes - I would recommend to start with no.2 to get the framework ready, and only then add multioutput support for some classifiers, e.g., the neural networks. That way, no.1 will also be a test case for the framework extensions in no.2.

[Vasudeva-bit]

Kindly review the code and help me with the following:

1. If the format looks good, I shall extend regression base class as well.
2. I need to set the tag "capability:multioutput" to True to all the estimators that support it. Kindly mention estimators that you know can support multioutput. I will try to figure the rest. Now, only CNNClassifier's tag is set to True.

add multioutput support for some classifiers, e.g., the neural networks

Once I am done with the above two, I shall continue with this. @fkiraly

[fkiraly]

Thanks!
This looks like it works almost.

There's something upset with the tags, can you check the tests?

Also, non-blocking, do you think we can avoid introducing an "instance" copy of every method, without making the code less DRY? I don't see it, but it might be worth thinking briefly about this.

[Vasudeva-bit]

There's something upset with the tags, can you check the tests?

Also, non-blocking, do you think we can avoid introducing an "instance" copy of every method, without making the code less DRY? I don't see it, but it might be worth thinking briefly about this.

I shall look into these.

[fkiraly]

I think they break. I will check that again.

Well, if they break, they should not get the multioutput tag until they are upgraded.

[fkiraly]

All updated now. I removed the tags from classifiers, we can do that separately.