Categorical data support (part 2)

This is a follow-up to https://github.com/dmlc/xgboost/issues/6503 .

# Hyper-parameters
- [ ] Large scale benchmarks.
- [ ] Investigate different parameters for preventing overfitting. (https://github.com/dmlc/xgboost/pull/7957)
- [ ] Compare results between different implementations.
- [ ] Produce documents about how each parameter affects model performance.

# Performance
- [ ] Optimize GPU evaluation function.
- [ ] Optimize CPU evaluation function by iterating only half of the histogram.
- [ ] Better handling for dataframe https://github.com/microsoft/LightGBM/issues/4596 https://github.com/dmlc/xgboost/pull/8653.

# Features
- [ ] Investigate the potential support for the exact tree method.
- [ ] Possible roadmap for other algorithms.
- [x] Missing value handling. (#7917, https://github.com/dmlc/xgboost/pull/7948, https://github.com/dmlc/xgboost/pull/7937, https://github.com/dmlc/xgboost/pull/7934, https://github.com/dmlc/xgboost/pull/8212)
- [x] Add demonstration to JSON model parser. (https://github.com/dmlc/xgboost/pull/8401)
- [ ] PySpark (https://github.com/dmlc/xgboost/issues/8398)

# 3-party libraries
We should have a simple function that's similar to our JSON parser example to export a Python model in XGBoost.
- [ ] SHAP https://github.com/slundberg/shap/issues/1302 https://github.com/shap/shap/issues/2662

# Language bindings
- [x] R. Need to support `factor`. (https://github.com/dmlc/xgboost/pull/8048, https://github.com/dmlc/xgboost/pull/9828)
- [ ] Java (#7966)
- [ ] Scala & Spark

Suggestions/discussions are welcomed!

Start by reading the linked follow-up issue #6503 and the unchecked sections in this issue. Review the referenced issues and pull requests for the parameter, performance, dataframe, algorithm, PySpark, SHAP, Java, and Scala/Spark work. Done is not defined as a single change; the relevant checklist item and its associated implementation or documentation would need to be completed.

Written by the indexing model from the issue text.