Conformal Prediction

This is a work in progress. I will be adding more content to this post in the coming days.

Reference: https://scikit-learn.org/stable/auto_examples/calibration/plot_calibration_multiclass.html#sphx-glr-auto-examples-calibration-plot-calibration-multiclass-py

import sklearn
import pandas as pd

import matplotlib.pyplot as plt
%matplotlib inline
%config InlineBackend.figure_format='retina'

import numpy as np
from sklearn.datasets import make_blobs

np.random.seed(0)

X, y = make_blobs(
    n_samples=2000, n_features=2, centers=3, random_state=42, cluster_std=5.0
)
X_train, y_train = X[:600], y[:600]
X_valid, y_valid = X[600:1000], y[600:1000]
X_train_valid, y_train_valid = X[:1000], y[:1000]
X_test, y_test = X[1000:], y[1000:]

# Scater plot showing different classes in different colors
plt.scatter(X[:, 0], X[:, 1], c=y ,alpha=0.7)

<matplotlib.collections.PathCollection at 0x1b19a5f70>

from sklearn.linear_model import LogisticRegression
lr = LogisticRegression()
lr.fit(X_train, y_train)

LogisticRegression()

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prob_df = pd.DataFrame(lr.predict_proba(X_valid))
prob_df.columns = lr.classes_
prob_df.head()

	0	1	2
0	0.014323	0.959135	0.026542
1	0.000326	0.004617	0.995057
2	0.667887	0.322486	0.009627
3	0.953779	0.043703	0.002518
4	0.000029	0.000130	0.999841

pd.Series(prob_df.values[np.arange(400), y_valid]).quantile(0.1)

0.3934260593598625

# Get the predicted probability for the correct class for each sample
y_valid

array([1, 2, 0, 0, 2, 2, 2, 1, 1, 2, 1, 1, 0, 1, 2, 0, 0, 1, 2, 1, 1, 2,
       1, 0, 0, 2, 0, 0, 1, 2, 0, 1, 2, 0, 0, 2, 1, 2, 0, 1, 1, 0, 0, 1,
       0, 0, 2, 2, 1, 1, 0, 0, 0, 1, 2, 2, 2, 1, 0, 1, 1, 1, 2, 0, 1, 1,
       0, 1, 1, 2, 2, 1, 0, 1, 1, 0, 2, 1, 2, 2, 2, 1, 2, 1, 1, 2, 2, 1,
       0, 1, 0, 1, 2, 2, 0, 0, 0, 1, 0, 1, 2, 2, 0, 2, 0, 2, 1, 0, 0, 1,
       2, 2, 2, 1, 0, 2, 2, 0, 0, 2, 0, 1, 2, 0, 1, 1, 2, 2, 1, 1, 2, 2,
       0, 0, 0, 0, 0, 0, 2, 0, 1, 1, 1, 2, 0, 2, 0, 1, 1, 0, 2, 0, 1, 0,
       1, 0, 2, 2, 0, 0, 2, 1, 0, 2, 0, 2, 0, 0, 0, 1, 2, 0, 1, 2, 0, 2,
       1, 0, 0, 0, 0, 2, 2, 1, 0, 2, 1, 1, 2, 0, 2, 0, 1, 2, 1, 1, 0, 0,
       2, 0, 1, 1, 1, 1, 0, 2, 2, 1, 1, 1, 0, 2, 1, 2, 2, 2, 1, 0, 0, 2,
       0, 0, 2, 2, 0, 2, 2, 2, 0, 1, 2, 0, 2, 0, 1, 0, 2, 2, 2, 1, 0, 1,
       1, 2, 2, 0, 2, 2, 2, 2, 0, 2, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 1,
       0, 1, 0, 1, 2, 0, 1, 2, 2, 2, 0, 1, 0, 1, 0, 1, 1, 2, 1, 1, 2, 0,
       1, 0, 1, 2, 0, 1, 0, 1, 1, 2, 0, 1, 1, 0, 2, 2, 1, 2, 0, 1, 1, 2,
       1, 2, 2, 0, 2, 2, 2, 0, 1, 2, 1, 0, 2, 1, 2, 0, 2, 1, 0, 1, 1, 2,
       0, 1, 2, 0, 2, 1, 2, 0, 0, 0, 2, 1, 0, 1, 0, 2, 1, 0, 1, 2, 0, 1,
       0, 1, 0, 2, 1, 1, 1, 2, 2, 0, 2, 2, 2, 1, 2, 1, 2, 2, 0, 0, 2, 2,
       0, 1, 1, 0, 1, 2, 0, 1, 1, 2, 1, 0, 1, 0, 0, 2, 2, 0, 0, 1, 0, 0,
       2, 2, 2, 2])

# Get the predicted probability for the correct class for each sample

	1	2	0	0	2	2	2	1	1	2	...	2	0	0	1	0	0	2	2	2	2
0	0.959135	0.026542	0.014323	0.014323	0.026542	0.026542	0.026542	0.959135	0.959135	0.026542	...	0.026542	0.014323	0.014323	0.959135	0.014323	0.014323	0.026542	0.026542	0.026542	0.026542
1	0.004617	0.995057	0.000326	0.000326	0.995057	0.995057	0.995057	0.004617	0.004617	0.995057	...	0.995057	0.000326	0.000326	0.004617	0.000326	0.000326	0.995057	0.995057	0.995057	0.995057
2	0.322486	0.009627	0.667887	0.667887	0.009627	0.009627	0.009627	0.322486	0.322486	0.009627	...	0.009627	0.667887	0.667887	0.322486	0.667887	0.667887	0.009627	0.009627	0.009627	0.009627
3	0.043703	0.002518	0.953779	0.953779	0.002518	0.002518	0.002518	0.043703	0.043703	0.002518	...	0.002518	0.953779	0.953779	0.043703	0.953779	0.953779	0.002518	0.002518	0.002518	0.002518
4	0.000130	0.999841	0.000029	0.000029	0.999841	0.999841	0.999841	0.000130	0.000130	0.999841	...	0.999841	0.000029	0.000029	0.000130	0.000029	0.000029	0.999841	0.999841	0.999841	0.999841
...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...	...
395	0.253215	0.038669	0.708116	0.708116	0.038669	0.038669	0.038669	0.253215	0.253215	0.038669	...	0.038669	0.708116	0.708116	0.253215	0.708116	0.708116	0.038669	0.038669	0.038669	0.038669
396	0.000339	0.999576	0.000086	0.000086	0.999576	0.999576	0.999576	0.000339	0.000339	0.999576	...	0.999576	0.000086	0.000086	0.000339	0.000086	0.000086	0.999576	0.999576	0.999576	0.999576
397	0.019843	0.980018	0.000139	0.000139	0.980018	0.980018	0.980018	0.019843	0.019843	0.980018	...	0.980018	0.000139	0.000139	0.019843	0.000139	0.000139	0.980018	0.980018	0.980018	0.980018
398	0.000094	0.999780	0.000126	0.000126	0.999780	0.999780	0.999780	0.000094	0.000094	0.999780	...	0.999780	0.000126	0.000126	0.000094	0.000126	0.000126	0.999780	0.999780	0.999780	0.999780
399	0.000133	0.999776	0.000092	0.000092	0.999776	0.999776	0.999776	0.000133	0.000133	0.999776	...	0.999776	0.000092	0.000092	0.000133	0.000092	0.000092	0.999776	0.999776	0.999776	0.999776

400 rows × 400 columns