Tutorial: Scorecard with continuous target

In this tutorial, we show that the use of scorecards is not limited to binary classification problems. We develop a scorecard using the Huber regressor as an estimator. The dataset for this tutorial is https://scikit-learn.org/stable/modules/generated/sklearn.datasets.fetch_california_housing.html.

[1]:

import matplotlib.pyplot as plt
import pandas as pd

from sklearn.datasets import fetch_california_housing
from sklearn.linear_model import HuberRegressor

from optbinning import BinningProcess
from optbinning import Scorecard

Load the dataset.

[2]:

data = fetch_california_housing()

target = "target"
variable_names = data.feature_names
X = pd.DataFrame(data.data, columns=variable_names)
y = data.target

[3]:

X.head()

[3]:
MedInc HouseAge AveRooms AveBedrms Population AveOccup Latitude Longitude
0 8.3252 41.0 6.984127 1.023810 322.0 2.555556 37.88 -122.23
1 8.3014 21.0 6.238137 0.971880 2401.0 2.109842 37.86 -122.22
2 7.2574 52.0 8.288136 1.073446 496.0 2.802260 37.85 -122.24
3 5.6431 52.0 5.817352 1.073059 558.0 2.547945 37.85 -122.25
4 3.8462 52.0 6.281853 1.081081 565.0 2.181467 37.85 -122.25

Then, we instantiate a BinningProcess object class with variable names.

[4]:

binning_process = BinningProcess(variable_names)

We select a robust linear model as an estimator.

[5]:

estimator = HuberRegressor(max_iter=200)

Finally, we instantiate a Scorecard class with the target name, a binning process object, and an estimator. In addition, we want to apply a scaling method to the scorecard points. Also, we select the reverse scorecard mode, so the score increases as the average house value increases.

[6]:

scorecard = Scorecard(binning_process=binning_process,
                      estimator=estimator, scaling_method="min_max",
                      scaling_method_params={"min": 0, "max": 100},
                      reverse_scorecard=True)

[7]:

scorecard.fit(X, y)

[7]:

Scorecard(binning_process=BinningProcess(variable_names=['MedInc', 'HouseAge',
                                                         'AveRooms',
                                                         'AveBedrms',
                                                         'Population',
                                                         'AveOccup', 'Latitude',
                                                         'Longitude']),
          estimator=HuberRegressor(max_iter=200), reverse_scorecard=True,
          scaling_method='min_max',
          scaling_method_params={'max': 100, 'min': 0})
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Similar to other objects in OptBinning, we can print overview information about the options settings, problems statistics, and the number of selected variables after the binning process.

[8]:

scorecard.information(print_level=2)

optbinning (Version 1.0.0)
Copyright (c) 2019-2026 Guillermo Navas-Palencia, Apache License 2.0

  Begin options
    binning_process                      yes   * U
    estimator                            yes   * U
    scaling_method                   min_max   * U
    scaling_method_params                yes   * U
    intercept_based                    False   * d
    reverse_scorecard                   True   * U
    rounding                           False   * d
    verbose                            False   * d
  End options

  Statistics
    Number of records                  20640
    Number of variables                    8
    Target type                   continuous

    Number of numerical                    8
    Number of categorical                  0
    Number of selected                     8

  Timing
    Total time                          2.43 sec
    Binning process                     1.87 sec   ( 76.76%)
    Estimator                           0.38 sec   ( 15.66%)
    Build scorecard                     0.05 sec   (  2.08%)
      rounding                          0.00 sec   (  0.01%)

Two scorecard styles are available: style="summary" shows the variable name, and their corresponding bins and assigned points; style="detailed" adds information from the corresponding binning table.

[9]:

scorecard.table(style="summary")

[9]:
Variable Bin Points
0 MedInc (-inf, 1.90) 9.971931
1 MedInc [1.90, 2.16) 11.050459
2 MedInc [2.16, 2.37) 11.665492
3 MedInc [2.37, 2.66) 12.845913
4 MedInc [2.66, 2.88) 13.896692
... ... ... ...
3 Longitude [-120.80, -119.76) 5.777181
4 Longitude [-119.76, -118.91) 6.182494
5 Longitude [-118.91, inf) 9.043458
6 Longitude Special 1.059686
7 Longitude Missing 1.059686

94 rows × 3 columns

[10]:

scorecard.table(style="detailed")

[10]:
Variable Bin id Bin Count Count (%) Sum Std Mean Min Max Zeros count WoE IV Coefficient Points
0 MedInc 0 (-inf, 1.90) 2039 0.098789 2240.75810 0.711884 1.098950 0.14999 5.00001 0 -0.969609 0.095786 0.919860 9.971931
1 MedInc 1 [1.90, 2.16) 1109 0.053731 1366.22203 0.663722 1.231941 0.14999 5.00001 0 -0.836618 0.044952 0.919860 11.050459
2 MedInc 2 [2.16, 2.37) 1049 0.050824 1371.86004 0.706034 1.307779 0.17500 5.00001 0 -0.760779 0.038666 0.919860 11.665492
3 MedInc 3 [2.37, 2.66) 1551 0.075145 2254.12108 0.704002 1.453334 0.30000 5.00001 0 -0.615224 0.046231 0.919860 12.845913
4 MedInc 4 [2.66, 2.88) 1075 0.052083 1701.62105 0.756965 1.582903 0.22500 5.00001 0 -0.485655 0.025295 0.919860 13.896692
... ... ... ... ... ... ... ... ... ... ... ... ... ... ... ...
3 Longitude 3 [-120.80, -119.76) 1100 0.053295 1420.05208 0.793982 1.290956 0.28300 5.00001 0 -0.777602 0.041442 0.414488 5.777181
4 Longitude 4 [-119.76, -118.91) 1221 0.059157 1711.68530 1.074386 1.401872 0.26600 5.00001 0 -0.666687 0.039439 0.414488 6.182494
5 Longitude 5 [-118.91, inf) 10839 0.525145 23680.86379 1.119555 2.184783 0.14999 5.00001 0 0.116225 0.061035 0.414488 9.043458
6 Longitude 6 Special 0 0.000000 0.00000 NaN 0.000000 NaN NaN 0 -2.068558 0.000000 0.414488 1.059686
7 Longitude 7 Missing 0 0.000000 0.00000 NaN 0.000000 NaN NaN 0 -2.068558 0.000000 0.414488 1.059686

94 rows × 15 columns

Compute score and predicted target using the fitted estimator.

[11]:

score = scorecard.score(X)

[12]:

y_pred = scorecard.predict(X)

The following plot shows a perfect linear relationship between the score and average the house value.

[13]:

plt.scatter(score, y, alpha=0.01, label="Average house value")
plt.plot(score, y_pred, label="Huber regression", linewidth=2, color="orange")
plt.ylabel("Average house value (unit=100,000)")
plt.xlabel("Score")
plt.legend()
plt.show()
../_images/tutorials_tutorial_scorecard_continuous_target_22_0.png