In the post (https://statcompute.wordpress.com/2018/11/23/more-robust-monotonic-binning-based-on-isotonic-regression), a more robust version of monotonic binning based on the isotonic regression was introduced. Nonetheless, due to the loss of granularity, the predictability has been somewhat compromised, which is a typical dilemma in the data science. On one hand, we don’t want to use a learning algorithm that is too greedy and therefore over-fits the data at the cost of simplicity and generality. On the other hand, we’d also like to get the most predictive power out of our data for better business results.
It is worth mentioning that, although there is a consensus that advancedensemble algorithms are able to significantly improve the prediction outcome, both bagging and boosting would also destroy the simple structure of binning outputs and therefore might not be directly applicable in this simple case.
In light of above considerations, the bumping (Bootstrap Umbrella of Model Parameters) procedure, which was detailed in Model Search And Inference By Bootstrap Bumping by Tibshirani and Knight (1997), should serve our dual purposes. First of all, since the final binning structure would be derived from an isotonic regression based on the bootstrap sample, the concern about over-fitting the original training data can be addressed. Secondly, through the bumping search across all bootstrap samples, chances are that a closer-to-optimal solution can be achieved. It is noted that, since the original sample is always included in the bumping procedure, a binning outcome with bumping that is at least as good as the one without is guaranteed.
The R function bump_bin() is my effort of implementing the bumping procedure on top of the monotonic binning function based on isotonic regression. Because of the mutual independence of binning across all bootstrap samples, the bumping is a perfect use case of parallelism for the purpose of faster execution, as demonstrated in the function.
The output below shows the bumping result based on 20 bootstrap samples. There is a small improvement in the information value, e.g. 0.8055 vs 0.8021 without bumping, implying a potential opportunity of bumping with a simpler binning structure, e.g. 12 bins vs 20 bins.
The output below is based on bumping with 200 bootstrap samples. The information value has been improved by 2%, e.g. 0.8174 vs 0.8021, with a lower risk of over-fitting, e.g. 14 bins vs 20 bins.
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