OptBinning is a library written in Python implementing a rigorous and flexible mathematical programming formulation to solving the optimal binning problem for a binary, continuous and multiclass target type, incorporating constraints not previously addressed.
Website: http://gnpalencia.org/optbinning/
Paper: Optimal binning: mathematical programming formulation. http://arxiv.org/abs/2001.08025
To install the current release of OptBinning:
pip install optbinning
To install from source, download or clone the git repository
git clone https://github.com/guillermo-navas-palencia/optbinning.git
cd optbinning
python setup.py install
If your are new to OptBinning, you can get started following the tutorials.
Let's load a well-known dataset from the UCI repository and choose a variable to discretize and the binary target.
import pandas as pd
from sklearn.datasets import load_breast_cancer
data = load_breast_cancer()
df = pd.DataFrame(data.data, columns=data.feature_names)
variable = "mean radius"
x = df[variable].values
y = data.targetImport and instantiate an OptimalBinning object class. We pass the variable name, its data type, and a solver, in this case, we choose the constraint programming solver. Fit the optimal binning object with arrays x and y.
from optbinning import OptimalBinning
optb = OptimalBinning(name=variable, dtype="numerical", solver="cp")
optb.fit(x, y)Check status and retrieve optimal split points
>>> optb.status
'OPTIMAL'
>>> optb.splits
array([11.42500019, 12.32999992, 13.09499979, 13.70499992, 15.04500008,
16.92500019])The optimal binning algorithms return a binning table; a binning table displays the binned data and several metrics for each bin. Call the method build, which returns a pandas.DataFrame.
>>> optb.binning_table.build() Bin Count Count (%) Non-event Event Event rate WoE IV JS
0 [-inf, 11.43) 118 0.207381 3 115 0.974576 -3.12517 0.962483 0.087205
1 [11.43, 12.33) 79 0.138840 3 76 0.962025 -2.71097 0.538763 0.052198
2 [12.33, 13.09) 68 0.119508 7 61 0.897059 -1.64381 0.226599 0.025513
3 [13.09, 13.70) 49 0.086116 10 39 0.795918 -0.839827 0.052131 0.006331
4 [13.70, 15.05) 83 0.145870 28 55 0.662651 -0.153979 0.003385 0.000423
5 [15.05, 16.93) 54 0.094903 44 10 0.185185 2.00275 0.359566 0.038678
6 [16.93, inf) 118 0.207381 117 1 0.008475 5.28332 2.900997 0.183436
7 Special 0 0.000000 0 0 0.000000 0 0.000000 0.000000
8 Missing 0 0.000000 0 0 0.000000 0 0.000000 0.000000
Totals 569 1.000000 212 357 0.627417 5.043925 0.393784
You can use the method plot to visualize the histogram and WoE or event rate curve. Note that the Bin ID corresponds to the binning table index.
>>> optb.binning_table.plot(metric="woe")
Now that we have checked the binned data, we can transform our original data into WoE or event rate values.
x_transform_woe = optb.transform(x, metric="woe")
x_transform_event_rate = optb.transform(x, metric="event_rate")The analysis method performs a statistical analysis of the binning table, computing the statistics Gini index, Information Value (IV), Jensen-Shannon divergence, and the quality score. Additionally, several statistical significance tests between consecutive bins of the contingency table are performed.
>>> optb.binning_table.analysis()---------------------------------------------
OptimalBinning: Binary Binning Table Analysis
---------------------------------------------
General metrics
Gini index 0.87541620
IV (Jeffrey) 5.04392547
JS (Jensen-Shannon) 0.39378376
HHI 0.15727342
HHI (normalized) 0.05193260
Cramer's V 0.80066760
Quality score 0.00000000
Significance tests
Bin A Bin B t-statistic p-value P[A > B] P[B > A]
0 1 0.252432 6.153679e-01 0.684380 3.156202e-01
1 2 2.432829 1.188183e-01 0.948125 5.187465e-02
2 3 2.345804 1.256207e-01 0.937874 6.212635e-02
3 4 2.669235 1.023052e-01 0.955269 4.473083e-02
4 5 29.910964 4.523477e-08 1.000000 9.814594e-12
5 6 19.324617 1.102754e-05 0.999999 1.216668e-06
Print overview information about the options settings, problem statistics, and the solution of the computation.
>>> optb.information(print_level=2)optbinning (Version 0.4.0)
Copyright (c) 2019-2020 Guillermo Navas-Palencia, Apache License 2.0
Begin options
name mean radius * U
dtype numerical * d
prebinning_method cart * d
solver cp * d
max_n_prebins 20 * d
min_prebin_size 0.05 * d
min_n_bins no * d
max_n_bins no * d
min_bin_size no * d
max_bin_size no * d
min_bin_n_nonevent no * d
max_bin_n_nonevent no * d
min_bin_n_event no * d
max_bin_n_event no * d
monotonic_trend auto * d
min_event_rate_diff 0 * d
max_pvalue no * d
max_pvalue_policy consecutive * d
gamma 0 * d
class_weight no * d
cat_cutoff no * d
user_splits no * d
special_codes no * d
split_digits no * d
mip_solver bop * d
time_limit 100 * d
verbose False * d
End options
Name : mean radius
Status : OPTIMAL
Pre-binning statistics
Number of pre-bins 9
Number of refinements 1
Solver statistics
Type cp
Number of booleans 26
Number of branches 58
Number of conflicts 0
Objective value 5043922
Best objective bound 5043922
Timing
Total time 0.06 sec
Pre-processing 0.00 sec ( 0.80%)
Pre-binning 0.00 sec ( 6.30%)
Solver 0.06 sec ( 91.45%)
model generation 0.05 sec ( 89.12%)
optimizer 0.01 sec ( 10.88%)
Post-processing 0.00 sec ( 0.12%)
The following table shows how OptBinning compares to scorecardpy 0.1.9.1.1 on a selection of variables from the public dataset, Home Credit Default Risk - Kaggle’s competition Link. This dataset contains 307511 samples.The experiments were run on Intel(R) Core(TM) i5-3317 CPU at 1.70GHz, using a single core, running Linux. For scorecardpy, we use default settings only increasing the maximum number of bins bin_num_limit=20. For OptBinning, we use default settings (max_n_prebins=20) only changing the maximum allowed p-value between consecutive bins, max_pvalue=0.05.
To compare softwares we use the shifted geometric mean, typically used in mathematical optimization benchmarks: http://plato.asu.edu/bench.html. Using the shifted (by 1 second) geometric mean we found that OptBinning is 17x faster than scorecardpy, with an average IV increase of 12%. Besides the speed and IV gains, OptBinning includes many more constraints and monotonicity options.
| Variable | scorecardpy_time | scorecardpy_IV | optbinning_time | optbinning_IV |
|---|---|---|---|---|
| AMT_INCOME_TOTAL | 6.18 s | 0.010606 | 0.363 s | 0.011705 |
| NAME_CONTRACT_TYPE (C) | 3.72 s | 0.015039 | 0.148 s | 0.015039 |
| AMT_CREDIT | 7.10 s | 0.053593 | 0.634 s | 0.059311 |
| ORGANIZATION_TYPE (C) | 6.31 s | 0.063098 | 0.274 s | 0.071520 |
| AMT_ANNUITY | 6.51 s | 0.024295 | 0.648 s | 0.031179 |
| AMT_GOODS_PRICE | 6.95 s | 0.056923 | 0.401 s | 0.092032 |
| NAME_HOUSING_TYPE (C) | 3.57 s | 0.015055 | 0.140 s | 0.015055 |
| REGION_POPULATION_RELATIVE | 4.33 s | 0.026578 | 0.392 s | 0.035567 |
| DAYS_BIRTH | 5.18 s | 0.081270 | 0.564 s | 0.086539 |
| OWN_CAR_AGE | 4.85 s | 0.021429 | 0.055 s | 0.021890 |
| OCCUPATION_TYPE (C) | 4.24 s | 0.077606 | 0.201 s | 0.079540 |
| APARTMENTS_AVG | 5.61 s | 0.032247(*) | 0.184 s | 0.032415 |
| BASEMENTAREA_AVG | 5.14 s | 0.022320 | 0.119 s | 0.022639 |
| YEARS_BUILD_AVG | 4.49 s | 0.016033 | 0.055 s | 0.016932 |
| EXT_SOURCE_2 | 5.21 s | 0.298463 | 0.606 s | 0.321417 |
| EXT_SOURCE_3 | 5.08 s | 0.316352 | 0.303 s | 0.334975 |
| TOTAL | 84.47 s | 1.130907 | 5.087 s | 1.247756 |
(C): categorical variable. (*): max p-value between consecutive bins > 0.05.
If you use OptBinning in your research/work, please cite the paper using the following BibTeX:
@article{Navas-Palencia2020OptBinning,
title = {Optimal binning: mathematical programming formulation},
author = {Guillermo Navas-Palencia},
year = {2020},
eprint = {2001.08025},
archivePrefix = {arXiv},
primaryClass = {cs.LG},
volume = {abs/2001.08025},
url = {http://arxiv.org/abs/2001.08025},
}