# A Summary of My Home-Brew Binning Algorithms for Scorecard Development

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Thus far, I have published four different monotonic binning algorithms for the scorecard development and think that it might be a right timing to do a quick summary. R functions for these binning algorithms are also available on https://github.com/statcompute/MonotonicBinning.

The first one was posted back in 2017 (https://statcompute.wordpress.com/2017/01/22/monotonic-binning-with-smbinning-package) based on my SAS macro (https://statcompute.wordpress.com/2012/06/10/a-sas-macro-implementing-monotonic-woe-transformation-in-scorecard-development) that has been widely used by sasORs. This R function mono_bin() is designed to generate monotonic bins with roughly equal densities, e.g. size of records in each bin. There are two potential issues for this binning algorithm. Albeit robust, the binning outcome is too coarse and and therefore might not be granular enough to capture the data nature. In addition, although the algorithm is fully automatic and able to converge globally, it requires iterations that might be computationally expensive for big datasets.

In light of aforementioned shortcomings, I developed the second one based on the isotonic regression (https://statcompute.wordpress.com/2017/06/15/finer-monotonic-binning-based-on-isotonic-regression and https://statcompute.wordpress.com/2018/11/23/more-robust-monotonic-binning-based-on-isotonic-regression) that successfully addresses both the coarse binning and iterations.

The third one was developed last year just out of my own curiosity (https://statcompute.wordpress.com/2018/10/14/monotonic-binning-with-equal-sized-bads-for-scorecard-development) for the purpose to generate monotonic bins with roughly equal-sized bads, e.g. Y = 1. From the performance standpoint, this one is not materially different from the first one. It is more like a brainteaser for myself.

The last one (https://statcompute.wordpress.com/2018/11/25/improving-binning-by-bootstrap-bumping) was mainly motivated by the idea of Bootstrap Bumping from Tibshirani and Knight (1997) and implements the bumping on top of the second one above based on the isotonic regression. The outcome of this one is satisfactory in two folds. First of all, since the bumping is based on bootstrap samples drawn from the original dataset, the concern about over-fitting due to the sample bias can be somewhat addressed. Secondly, through the bumping search across all bootstrap samples, chances are that a closer-to-optimal solution can be achieved.

R functions for all 4 binning algorithms on the GitHub are built on top of an utility function manual_bin() (https://github.com/statcompute/MonotonicBinning/blob/master/code/manual_bin.R). In the R code, I tried my best to make it as generic as possible without importing additional packages. The only exception is that the parallel package is used in the bump_bin() function to speed up the computation. My next task might be writing a scoring function to make these binning algorithms useful in production.

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