Today, give a try to Techtonique web app, a tool designed to help you make informed, data-driven decisions using Mathematics, Statistics, Machine Learning, and Data Visualization. Here is a tutorial with audio, video, code, and slides: https://moudiki2.gumroad.com/l/nrhgb. 100 API requests are now (and forever) offered to every user every month, no matter the pricing tier.
In this post, I use the following Python packages:
-
BCN
: for adjusting Boosted Configuration Networks regression (see post 1 and post 2 for more details on BCNs, and this notebook for classification examples) tosklearn
’sdiabetes
dataset. -
the-teller
: for interpreting BCNs, and obtaining prediction intervals. So far, as of october 2022,the-teller
contains two methods for constructing prediction intervals: split conformal and local conformal. For more details on both of these methods, the interested reader can consult [1]. Despite their potential drawbacks (listed in [1]), they’re model-agnostic, i.e they do not require in particular for the user to adjust a quantile regression model.
Content
- 0 - Install packages
- 1 - Import packages + load data
- 2 - Adjust BCN model to training set, evaluation on test set
- 3 - Adjust the teller’s Explainer to test set
- 4 - Prediction intervals on test set
- 4 - 1 Split conformal
- 4 - 2 Local conformal
- 5 - Plot prediction intervals
0 - Install packages
Package implementing Boosted Configuration Networks
pip install BCN
Package for Machine Learning Explainability on tabular data
pip install the-teller
Other packages
pip install scikit-learn numpy
1 - Import packages + load data
import BCN as bcn # takes a long time to run, ONLY the first time it's run
import teller as tr
import numpy as np
from sklearn.datasets import load_diabetes
from sklearn.model_selection import train_test_split
from sklearn import metrics
from time import time
import diabetes
dataset
dataset = load_diabetes()
X = dataset.data
y = dataset.target
# split data into training test and test set
X_train, X_test, y_train, y_test = train_test_split(X, y,
test_size=0.2, random_state=13)
2 - Adjust BCN model to training set, evaluation on test set
start = time()
regr_bcn = bcn.BCNRegressor(**{'B': 122,
'nu': 0.7862040612242153,
'col_sample': 0.6797268557618982,
'lam': 0.9244772287770061,
'r': 0.18915458607547728,
'tol': 9.670499926559012e-10})
regr_bcn.fit(X_train, y_train)
print(f"\nElapsed {time() - start}")
preds = regr_bcn.predict(X_test)
# Test set RMSE
print(np.sqrt(np.mean(np.square(y_test - preds))))
Elapsed 0.641953706741333
54.50979209778048
3 - Adjust the teller’s Explainer to test set
start = time()
# creating an Explainer for the fitted object `regr_bcn`
expr = tr.Explainer(obj=regr_bcn)
# confidence int. and tests on covariates' effects (Jackknife)
expr.fit(X_test, y_test, X_names=dataset.feature_names, method="ci")
# summary of results
expr.summary()
# timing
print(f"\n Elapsed: {time()-start}")
Score (rmse):
54.51
Residuals:
Min 1Q Median 3Q Max
-119.79528 -30.293474 9.749065 45.169791 124.891462
Tests on marginal effects (Jackknife):
Estimate Std. Error 95% lbound 95% ubound Pr(>|t|)
bmi 534.170652 10.538064 513.228463 555.11284 0.0 ***
s5 460.090298 11.7154 436.808403 483.372194 0.0 ***
bp 245.510926 7.073121 231.454584 259.567267 0.0 ***
s6 117.899033 8.865569 100.280578 135.517488 0.0 ***
s4 71.20425 4.885591 61.495165 80.913336 0.0 ***
age 3.144209 7.616405 -11.991795 18.280213 0.680742 -
s1 -31.76086 8.823018 -49.294754 -14.226967 0.000526 ***
s2 -104.139443 8.596589 -121.223357 -87.055529 0.0 ***
sex -167.461194 3.92965 -175.270546 -159.651841 0.0 ***
s3 -210.749954 5.580957 -221.840934 -199.658975 0.0 ***
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘-’ 1
Multiple R-squared: 0.394, Adjusted R-squared: 0.316
Elapsed: 0.1125936508178711
For more details on this output, you can read this post applying the-teller to xgboost’s explanation.
4 - Prediction intervals on test set
4 - 1 Split conformal
pi = tr.PredictionInterval(regr_bcn, method="splitconformal", level=0.95)
pi.fit(X_train, y_train)
preds = pi.predict(X_test, return_pi=True)
pred = preds[0]
y_lower = preds[1]
y_upper = preds[2]
print(len(pred))
# compute and display the average coverage
print(np.mean((y_test >= y_lower) & (y_test <= y_upper)))
# prediction interval's length
length_pi = y_upper - y_lower
print(np.mean(length_pi))
89
0.9438202247191011
209.55455918396666
4 - 2 Local conformal
pi2 = tr.PredictionInterval(regr_bcn, method="localconformal", level=0.95)
pi2.fit(X_train, y_train)
preds2 = pi2.predict(X_test, return_pi=True)
pred2 = preds2[0]
y_lower2 = preds2[1]
y_upper2 = preds2[2]
print(len(pred2))
# compute and display the average coverage
print(np.mean((y_test >= y_lower2) & (y_test <= y_upper2)))
# prediction interval's length
length_pi2 = y_upper2 - y_lower2
print(np.mean(length_pi2))
89
0.9550561797752809
229.03014949955275
5 - Plot prediction intervals
import warnings
warnings.filterwarnings('ignore')
import matplotlib
matplotlib.use('Agg')
import matplotlib.pyplot as plt
import numpy as np
np.warnings.filterwarnings('ignore')
split_color = 'tomato'
local_color = 'gray'
%matplotlib inline
np.random.seed(1)
def plot_func(x,
y,
y_u=None,
y_l=None,
pred=None,
shade_color="",
method_name="",
title=""):
fig = plt.figure()
plt.plot(x, y, 'k.', alpha=.3, markersize=10,
fillstyle='full', label=u'Test set observations')
if (y_u is not None) and (y_l is not None):
plt.fill(np.concatenate([x, x[::-1]]),
np.concatenate([y_u, y_l[::-1]]),
alpha=.3, fc=shade_color, ec='None',
label = method_name + ' Prediction interval')
if pred is not None:
plt.plot(x, pred, 'k--', lw=2, alpha=0.9,
label=u'Predicted value')
#plt.ylim([-2.5, 7])
plt.xlabel('$X$')
plt.ylabel('$Y$')
plt.legend(loc='upper right')
plt.title(title)
plt.show()
Split conformal
max_idx = 25
plot_func(x = range(max_idx),
y = y_test[0:max_idx],
y_u = y_upper[0:max_idx],
y_l = y_lower[0:max_idx],
pred = pred[0:max_idx],
shade_color=split_color,
title = f"Split conformal ({max_idx} first points in test set)")
Local conformal
max_idx = 25
plot_func(x = range(max_idx),
y = y_test[0:max_idx],
y_u = y_upper2[0:max_idx],
y_l = y_lower2[0:max_idx],
pred = pred2[0:max_idx],
shade_color=local_color,
title = f"Local conformal ({max_idx} first points in test set)")
[1] Romano, Y., Patterson, E., & Candes, E. (2019). Conformalized quantile regression. Advances in neural information processing systems, 32.
For attribution, please cite this work as:
T. Moudiki (2022-10-05). Prediction intervals (not only) for Boosted Configuration Networks in Python. Retrieved from https://thierrymoudiki.github.io/blog/2022/10/05/python/explainableml/interpretation-and-PI-for-BCN
BibTeX citation (remove empty spaces)@misc{ tmoudiki20221005, author = { T. Moudiki }, title = { Prediction intervals (not only) for Boosted Configuration Networks in Python }, url = { https://thierrymoudiki.github.io/blog/2022/10/05/python/explainableml/interpretation-and-PI-for-BCN }, year = { 2022 } }
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- Feedback forms for contributing Feb 7, 2020
- nnetsauce for R Jan 31, 2020
- A new version of nnetsauce (v0.3.1) Jan 24, 2020
- ESGtoolkit, a tool for Monte Carlo simulation (v0.2.0) Jan 17, 2020
- Search bar, new year 2020 Jan 10, 2020
- 2019 Recap, the nnetsauce, the teller and the querier Dec 20, 2019
- Understanding model interactions with the `teller` Dec 13, 2019
- Using the `teller` on a classifier Dec 6, 2019
- Benchmarking the querier's verbs Nov 29, 2019
- Composing the querier's verbs for data wrangling Nov 22, 2019
- Comparing and explaining model predictions with the teller Nov 15, 2019
- Tests for the significance of marginal effects in the teller Nov 8, 2019
- Introducing the teller Nov 1, 2019
- Introducing the querier Oct 25, 2019
- Prediction intervals for nnetsauce models Oct 18, 2019
- Using R in Python for statistical learning/data science Oct 11, 2019
- Model calibration with `crossval` Oct 4, 2019
- Bagging in the nnetsauce Sep 25, 2019
- Adaboost learning with nnetsauce Sep 18, 2019
- Change in blog's presentation Sep 4, 2019
- nnetsauce on Pypi Jun 5, 2019
- More nnetsauce (examples of use) May 9, 2019
- nnetsauce Mar 13, 2019
- crossval Mar 13, 2019
- test Mar 10, 2019
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