[python] add type hints on train() in engine.py

[jameslamb]

Proposes adding type hints on train(), as part of #3756.

[StrikerRUS]

Oh, that was a hard work, thanks!

sklearn-wrapper and hence Dask-package use callables with another signature for custom objective and metric functions:

LightGBM/python-package/lightgbm/sklearn.py

Lines 23 to 49 in 4e18c60

	This class transforms objective function to match objective function with signature ``new_func(preds, dataset)``
	as expected by ``lightgbm.engine.train``.
	Parameters
	----------
	func : callable
	Expects a callable with signature ``func(y_true, y_pred)`` or ``func(y_true, y_pred, group)
	and returns (grad, hess):
	y_true : array-like of shape = [n_samples]
	The target values.
	y_pred : array-like of shape = [n_samples] or shape = [n_samples * n_classes] (for multi-class task)
	The predicted values.
	Predicted values are returned before any transformation,
	e.g. they are raw margin instead of probability of positive class for binary task.
	group : array-like
	Group/query data.
	Only used in the learning-to-rank task.
	sum(group) = n_samples.
	For example, if you have a 100-document dataset with ``group = [10, 20, 40, 10, 10, 10]``, that means that you have 6 groups,
	where the first 10 records are in the first group, records 11-30 are in the second group, records 31-70 are in the third group, etc.
	grad : array-like of shape = [n_samples] or shape = [n_samples * n_classes] (for multi-class task)
	The value of the first order derivative (gradient) of the loss
	with respect to the elements of y_pred for each sample point.
	hess : array-like of shape = [n_samples] or shape = [n_samples * n_classes] (for multi-class task)
	The value of the second order derivative (Hessian) of the loss
	with respect to the elements of y_pred for each sample point.

LightGBM/python-package/lightgbm/sklearn.py

Lines 112 to 144 in 4e18c60

	This class transforms evaluation function to match evaluation function with signature ``new_func(preds, dataset)``
	as expected by ``lightgbm.engine.train``.
	Parameters
	----------
	func : callable
	Expects a callable with following signatures:
	``func(y_true, y_pred)``,
	``func(y_true, y_pred, weight)``
	or ``func(y_true, y_pred, weight, group)``
	and returns (eval_name, eval_result, is_higher_better) or
	list of (eval_name, eval_result, is_higher_better):
	y_true : array-like of shape = [n_samples]
	The target values.
	y_pred : array-like of shape = [n_samples] or shape = [n_samples * n_classes] (for multi-class task)
	The predicted values.
	In case of custom ``objective``, predicted values are returned before any transformation,
	e.g. they are raw margin instead of probability of positive class for binary task in this case.
	weight : array-like of shape = [n_samples]
	The weight of samples.
	group : array-like
	Group/query data.
	Only used in the learning-to-rank task.
	sum(group) = n_samples.
	For example, if you have a 100-document dataset with ``group = [10, 20, 40, 10, 10, 10]``, that means that you have 6 groups,
	where the first 10 records are in the first group, records 11-30 are in the second group, records 31-70 are in the third group, etc.
	eval_name : string
	The name of evaluation function (without whitespace).
	eval_result : float
	The eval result.
	is_higher_better : bool
	Is eval result higher better, e.g. AUC is ``is_higher_better``.

[jameslamb]

sklearn-wrapper and hence Dask-package use callables with another signature for custom objective and metric functions

oh interesting, all this time I didn't know that the interfaces were different!

I'll remove those changes from this PR and make them in a separate one.

[StrikerRUS]

I'll remove those changes from this PR and make them in a separate one.

Nice plan, thanks!

[StrikerRUS]

Great job, many thanks!

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