How to handle a regression problem with skewed target and only few high values?
You can generate symmetrical distribution(s) by suitable transformation:
Your distribution is mainly right-skewed, therefore a log10 transformation is required.
You can also use an auto-binning method and combine it with dummy variables for the spikes.
If you then perform a feature selection, the learner will automatically choose the most significant features. Learners like XGBoost automatically take care of multicollinearity.