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* Turn `early_stopping` into a Callable class

* Fix

* Lint

* Remove print

* Fix order

* Revert "Lint"

This reverts commit 7ca8b557572446888cf793c0082d9a7efd1e29a7.

* Apply suggestion from code review

* Nit

* Lint

* Move callable class outside the func for pickling

* Move _pickle and _unpickle to tests utils

* Add early stopping callback picklability test

* Nit

* Fix

* Lint

* Improve type hint

* Lint

* Lint

* Add cloudpickle to test_windows

* Update tests/python_package_test/test_engine.py

* Fix

* Apply suggestions from code review

* expose FeatureNumBin in C api

* parametrize min_data_in_bin and add test with max_bin_by_feature

* include feature_num_bin in R package

* add suggestion from review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* update error message and lint

* lint

* add call method

* minor improvements in tests

* add suggestions from review

* lint

* rename argument to feature in python and r packages
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* better logging of column datatypes

* update to checking function

* fix typo

* Update python-package/lightgbm/basic.py
Co-authored-by: José Morales <jmoralz92@gmail.com>

* Update python-package/lightgbm/basic.py
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>
Co-authored-by: José Morales <jmoralz92@gmail.com>
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

[python-package] [R-package] propagate the best iteration of cvbooster into the individual boosters (#5066)

* docs: booster eval methods accept list of callables

* docs: remove extra space

[python] fixes for supporting 2d numpy arrays for predictions, grads and hess in multiclass custom objective and eval (#5030)

* fixes for supporting 2d numpy arrays for predictions, grads and hess in multiclass custom objective

* Apply suggestions from code review
Co-authored-by: José Morales <jmoralz92@gmail.com>
Co-authored-by: José Morales <jmoralz92@gmail.com>

* map nullable dtypes to regular float dtypes

* cast x3 to float after introducing missing values

* add test for regular dtypes

* use .astype and then values. update nullable_dtypes test and include test for regular numpy dtypes

* more specific allowed dtypes. test no copy when single float dtype df

* use np.find_common_type. set np.float128 to None when it isn't supported

* set default as type(None)

* move tests that use lgb.train to test_engine

* include np.float32 when finding common dtype

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* add linebreak
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* docs: weight parameter non-negative

* docs: weights non negative only for train data

* docs: weights should be non negative for validation data

* typo in html render

* docs: brief weights non-negative description

[python-package] use 2d collections for predictions, grads and hess in multiclass custom objective (#4925)

* reshape predictions, grad and hess in multiclass custom objective

* add sklearn test. move custom obj to utils. docs for numpy

* use num_model_per_iteration to get num_classes

* update docs and dask multiclass custom objective test

* move reshaping to __inner_predict. add test for feval

* add missing note. remove extra line

* clarify that categoricals will be converted to ints and not that they should be ints in the input data

* update remaining sections

* update config.h

* add suggestions

* Update setup.py

* Update cuda.yml

* Update static_analysis.yml

* Update linkchecker.yml

* Update .appveyor.yml

* Update .vsts-ci.yml

* Update python_package.yml

* Update .vsts-ci.yml

* Update python_package.yml

* Update cuda.yml

* Update static_analysis.yml

* Update linkchecker.yml

* Update .vsts-ci.yml

* Update .appveyor.yml

* re-arange Python version

* make record_evaluation compatible with cv

* test multiple metrics in cv

* lint

* fix cv with train metric. save stdv as well

* always add dataset prefix to cv_agg

* remove unused function

[docs] document `conda-forge` channel preference over `default` one and describe possible workaround for OpenMP conflicts in FAQ (#4994)

* Update README.rst

* Update FAQ.rst

* Python FAQ entry about conda-forge

* fix syntax

* feat: refit additional kwargs for dataset and predict

* test: kwargs for refit method

* fix: __init__ got multiple values for argument

* fix: pycodestyle E302 error

* refactor: dataset_params to avoid breaking change

* refactor: expose all Dataset params in refit

* feat: dataset_params updates new_params

* fix: remove unnecessary params to test

* test: parameters input are the same

* docs: address StrikeRUS changes

* test: refit test changes in train dataset

* test: set init_score and decay_rate to zero

* add test for custom objective with regressor

* add test for custom binary classification objective with classifier

* isort

* got tests working for multiclass

* update docs

* train deeper model for classifier

* Apply suggestions from code review
Co-authored-by: José Morales <jmoralz92@gmail.com>

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* update multiclass tests

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* fix multiclass probabilities

* linting
Co-authored-by: José Morales <jmoralz92@gmail.com>
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* Update README.rst

* Update FAQ.rst

[python] raise an informative error instead of segfaulting when custom objective produces incorrect output (#4815)

* fix for bad grads causing segfault

* adjust checking criteria to properly reflect reality of multi-class classifiers

* fix styling

* Line break before operator

* Update python-package/lightgbm/basic.py
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* Update python-package/lightgbm/basic.py
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* add a note to the C-API docs

* rearrange text s;ightly

* add some tests to python package

* Update include/LightGBM/c_api.h
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* PR comments

* match argument is a regex and our expression has brackets ..

* rework tests

* isorting imports

* updating test to relfect that the python APi does not take pres/labels as a fobj function
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* Update test_sklearn.py

* Update python_package.yml

* Update python_package.yml

* Update callback.py

* Update callback.py

* Update sklearn.py

* Update sklearn.py

* Update test_sklearn.py

* Update .appveyor.yml

* Update .vsts-ci.yml

* Update python_package.yml

* Update setup.py

* Update test.sh

* Update .vsts-ci.yml

* Update .vsts-ci.yml

* Update Installation-Guide.rst

* Update install.libs.R

* Update setup.py

* Update r_package.yml

* Update install.libs.R

* remove `verbose_eval` argument

* update example Notebook

* [python-package][dask] handle failures parsing work host names

* add tests

* revert local testing changes

* unify values of `best_iteration` for sklearn and standard APIs

* update Dask test

* Update .vsts-ci.yml

* Update setup.sh

* Update .vsts-ci.yml

* Update test.sh

* Update README.rst

* add C API function that returns all param names with aliases

* add C API function that returns all param names with aliases

* add R code

* test R code

* remove debug CI

* fix R lint

* refactor

* run CI

* fix R

* fix

* revert CI checks

* revert changes in docs

* Try to make function `const`
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* add `const` in cpp file

* address review comments and sync with `master`
Co-authored-by: James Lamb <jaylamb20@gmail.com>

* [python-package] fix mypy errors in engine.py

* Apply suggestions from code review
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>

* allow for stdv

* whitespace
Co-authored-by: Nikita Titov <nekit94-08@mail.ru>