What are recommended methods for multi-task prediction? Currently, we are working on a school project which is trying to predict the number of crimes in some area/neighbourhood. 

There are 8 different categories for crimes and we've tried to find the correlation among those categories and now we only have 4 left. 
Instead of building a model for each category, we want to predict these 4 categories simultaneously by some multi-output algorithm.

Our sample size is around 27,000 for 6 years (from 2011 to 2016, 4000+ for each year). We are going to use (maybe) cross-validation to build/test our model.

Would you please list 2-3 algorithms which already have fully or partially implemented library in Python (preferred) or R you would recommend to use with our dataset scale?
I only found scikit-learn with this algorithm. But it's for classification rather then prediction numbers.

This is a intro-level ML course project, the group is not very experienced in the field and the time is limited so we don't want to implement an algorithm from scratch.
For the project, do you need to explain exactly how the input variables gave you the predictions? If so, trees based methods (R library 'tree', 'rpart') and Logistic Regression would be easy to explain to your stakeholder / lecturer.

If this explanation is not that important, or you could get by just showing the relative predictor importance, and you'd like to focus on accuracy. XGBoost is my default recommendation for multi-class predictions that I use at work on a daily basis. If XGBoost has too many parameters for your liking, you could try randomForest which only has 2 main parameters to tune. Both XGBoost and randomForest have functions for variable importance measures. (R Library XGBoost and randomForest)