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[python-package] remove 'fobj' in favor of passing custom objective function in params (fixes #3244) (#5052)

* feat: support custom metrics in params

* feat: support objective in params

* test: custom objective and metric

* fix: imports are incorrectly sorted

* feat: convert eval metrics str and set to list

* feat: convert single callable eval_metric to list

* test: single callable objective in params
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* feat: callable fobj in basic cv function
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: cv support objective callable
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix: assert in cv_res
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* docs: objective callable in params
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* recover test_boost_from_average_with_single_leaf_trees
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* linters fail
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* remove metrics helper functions
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* feat: choose objective through _choose_param_values
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: test objective through _choose_param_values
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: test objective is callabe in train
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: parametrize choose_param_value with objective aliases
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: cv booster metric is none
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix: if string and callable choose callable
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test train uses custom objective metrics
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: cv uses custom objective metrics
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: remove fobj parameter in train and cv
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: objective through params in sklearn API
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* custom objective function in advanced_example
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix whitespackes lint

* objective is none not a particular case for predict method
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* replace scipy.expit with custom implementation
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* test: set num_boost_round value to 20
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* fix: custom objective default_value is none
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: remove self._fobj
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* custom_objective default value is None
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* refactor: variables name reference dummy_obj
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* linter errors

* fix: process objective parameter when calling predict
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* linter errors

* fix: objective is None during predict call
Signed-off-by: Miguel Trejo <armando.trejo.marrufo@gmail.com>

* Reffer to string type as `str` and and commas in `list of ...` types

* update `libpath.py` too

* Improved the syntax of the fstrings

* Improved the strings to fstrings

* Reverted back the white space.

* Update examples/python-guide/advanced_example.py
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* Correct spelling

Most changes were in comments, and there were a few changes to literals for log output.

There were no changes to variable names, function names, IDs, or functionality.

* Clarify a phrase in a comment
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* Clarify a phrase in a comment
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* Clarify a phrase in a comment
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* Correct spelling

Most are code comments, but one case is a literal in a logging message.

There are a few grammar fixes too.
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* Update setup.py

* Update .appveyor.yml

* Update .travis.yml

* Update .vsts-ci.yml

* Update __init__.py

* Update test.sh

* Update test_windows.ps1

* Update advanced_example.py

* Update requirements_base.txt

* Update conf.py

* Update conf.py

* Update test_engine.py

* Update utils.py

* Update dockerfile-r

* Update README.md

* Update dockerfile.gpu

* Update test_consistency.py

* Update basic.py

* Update compat.py

* Update engine.py

* Update sklearn.py

* Update sklearn.py

* Update callback.py

* Update setup.py

* Update __init__.py

* Update plotting.py

* Update sklearn.py

* Update engine.py

* Update compat.py

* Update callback.py

* Update basic.py

* Update compat.py

* Update basic.py

* Update basic.py

* Update compat.py

* Update compat.py

* Update plotting.py

* Update engine.py

* Update basic.py

* Update sklearn.py

* Update compat.py

* Update engine.py

* Update engine.py

* Update callback.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update sklearn.py

* Update sklearn.py

* Update plotting.py

* Update sklearn.py

* Update compat.py

* Update compat.py

* Update engine.py

* Update plotting.py

* Update sklearn.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update compat.py

* Update compat.py

* Update compat.py

* Update engine.py

* Update basic.py

* Update compat.py

* Update basic.py

* Update basic.py

* Update basic.py

* Update compat.py

* Update compat.py

* Update basic.py

* Update basic.py

* Update .vsts-ci.yml

* Update .vsts-ci.yml

* Update conf.py

* Revert "Update dockerfile-r"

This reverts commit 4ff6ffc7e3eeda24cc6a59a3bb0c973f02d9d71c.

* added example about custom feval with sklearn wrapper

* fixed pylint

* added new example in contents

* unified run example commands for Windows and Linux

* added note about comments in examples conf files

* updated pep8 to pycodestyle

* fixed E722 do not use bare 'except'

* fixed W605 invalid escape sequence '\*'

* fixed W504 line break after binary operator

* ignore W605 invalid escape sequence '\*' in nuget builder

* made pycodestyle happy

* add python examples to test [test should fail]

* fix example && move some to advanced_example

* fix last line

* refine test python version

* Update Python-API.md

* for a better jump in page

A space is needed between `#` and the headers content according to Github's markdown format [guideline](https://guides.github.com/features/mastering-markdown/)

After adding the spaces, we can jump to the exact position in page by click the link.

* fixed something mentioned by @wxchan

* Update Python-API.md

* Add examples on how to use the saved model

* move 'load model' examples to advanced_example

* format python code with pep8

* **DO NOT MERGE** deliberately break rules to see what will happen during check

* Revert "**DO NOT MERGE** deliberately break rules to see what will happen during check"

This reverts commit 0db93cd7a43c7efa43a2112ada43d46c6f9115d9.

* fix format in test.py

* add docs for pep-8

add learning rate to dart (#133)