Probability calibration in ML Python - Model Metrics & Evaluation

Metrics & Evaluation - Probability calibration

Which metric matters for Probability Calibration and WHY

Probability calibration checks if the model's predicted chances match real outcomes. For example, if a model says 70% chance of rain, it should rain about 7 times out of 10 when it says that. The key metrics are Calibration Curve and Brier Score. The calibration curve shows how predicted probabilities compare to actual results. The Brier score measures the average squared difference between predicted probabilities and actual outcomes. Lower Brier scores mean better calibration.

Confusion Matrix or Equivalent Visualization

Probability calibration is about probabilities, not just yes/no predictions, so confusion matrix alone is not enough. Instead, we use a Calibration Curve which groups predictions by probability bins and compares predicted vs actual frequency.

Probability Bin | Predicted Probability | Actual Frequency
---------------------------------------------------------
     0.0 - 0.1 | 0.08                  | 0.07
     0.1 - 0.2 | 0.15                  | 0.18
     0.2 - 0.3 | 0.25                  | 0.22
     0.3 - 0.4 | 0.35                  | 0.33
     0.4 - 0.5 | 0.45                  | 0.48
     0.5 - 0.6 | 0.55                  | 0.52
     0.6 - 0.7 | 0.65                  | 0.68
     0.7 - 0.8 | 0.75                  | 0.73
     0.8 - 0.9 | 0.85                  | 0.88
     0.9 - 1.0 | 0.95                  | 0.94

This table shows predicted probabilities and how often the event actually happened in that range. Good calibration means these numbers are close.

Precision vs Recall Tradeoff and Calibration

Precision and recall focus on classification decisions (yes/no), but calibration focuses on how well predicted probabilities match reality. A model can have high precision and recall but poor calibration if its probabilities are too confident or too low. For example, a spam filter might catch spam well (high recall) but if it always says 99% spam chance even when unsure, it is poorly calibrated. Calibration helps trust the probability values, which is important for decisions like medical diagnosis or weather forecasts.

What Good vs Bad Calibration Looks Like

Good calibration: Predicted probabilities closely match actual outcomes. For example, when the model predicts 0.7 chance, the event happens about 70% of the time. The calibration curve is close to the diagonal line. Brier score is low (closer to 0).

Bad calibration: Predicted probabilities are too high or too low compared to actual outcomes. For example, the model predicts 0.9 chance but the event happens only 50% of the time. The calibration curve deviates far from the diagonal. Brier score is higher.

Common Pitfalls in Probability Calibration

• Ignoring calibration: Using raw probabilities without checking calibration can mislead decisions.
• Small sample sizes: Calibration curves can be noisy if there are few samples in probability bins.
• Overfitting calibration: Adjusting probabilities too much on training data can hurt performance on new data.
• Confusing accuracy with calibration: A model can be accurate in classification but poorly calibrated in probabilities.
• Data leakage: If calibration is done on data used for training, it gives overly optimistic results.

Self Check: Your model has 98% accuracy but poor calibration. Is it good?

Not necessarily. High accuracy means the model predicts the right class often, but if the predicted probabilities are not reliable, decisions based on those probabilities can be wrong. For example, if a medical test says 99% chance of disease but the real chance is only 50%, doctors might overreact. So, good calibration is important when you need trustworthy probability estimates, even if accuracy is high.

Key Result

Probability calibration is best measured by calibration curves and Brier score to ensure predicted probabilities match real outcomes.

Practice

1. What is the main goal of probability calibration in machine learning?

easy

A. To adjust predicted probabilities to better reflect true likelihoods

B. To increase the accuracy of class labels

C. To reduce the size of the training dataset

D. To speed up the training process

Solution

1. Step 1: Understand the purpose of probability calibration

   Probability calibration aims to make predicted probabilities match the actual chance of an event happening.

2. Step 2: Differentiate from accuracy and training speed

   Accuracy relates to correct labels, not probability quality. Calibration focuses on probability quality, not dataset size or speed.

3. Final Answer:

   To adjust predicted probabilities to better reflect true likelihoods -> Option A

4. Quick Check:

   Calibration = Adjust probabilities [OK]

Hint: Calibration fixes probability quality, not accuracy or speed [OK]

Common Mistakes:

• Confusing calibration with accuracy improvement
• Thinking calibration changes dataset size
• Assuming calibration speeds training

2. Which of the following is a common method used for probability calibration?

easy

A. K-means clustering

B. Gradient boosting

C. Platt scaling

D. Principal component analysis

Solution

1. Step 1: Identify calibration methods

   Platt scaling is a sigmoid-based method commonly used to calibrate probabilities.

2. Step 2: Exclude unrelated methods

   Gradient boosting is a model training technique, K-means is clustering, and PCA is dimensionality reduction, none are calibration methods.

3. Final Answer:

   Platt scaling -> Option C

4. Quick Check:

   Calibration method = Platt scaling [OK]

Hint: Remember Platt scaling for calibration, others are different tasks [OK]

Common Mistakes:

• Confusing boosting with calibration
• Mixing clustering or PCA with calibration
• Choosing any popular ML method as calibration

3. Given the following Python code using scikit-learn, what will be the output of calibrated_clf.predict_proba([[0.5, 1.5]])?

from sklearn.datasets import make_classification
from sklearn.linear_model import LogisticRegression
from sklearn.calibration import CalibratedClassifierCV

X, y = make_classification(n_samples=100, n_features=2, random_state=42)
clf = LogisticRegression().fit(X, y)
calibrated_clf = CalibratedClassifierCV(clf, method='sigmoid', cv='prefit')
calibrated_clf.fit(X, y)

probs = calibrated_clf.predict_proba([[0.5, 1.5]])
print(probs)

medium

A. A 2D array with calibrated probabilities for each class, e.g. [[0.3, 0.7]]

B. A single float value representing probability

C. An error because cv='prefit' requires a different fit method

D. A list of predicted class labels, e.g. [1]

Solution

1. Step 1: Understand CalibratedClassifierCV output

   Using method='sigmoid' with cv='prefit' fits calibration on the existing model and outputs probabilities as a 2D array for each class.

2. Step 2: Check predict_proba output format

   predict_proba returns probabilities for each class in a 2D array, not a single float or labels.

3. Final Answer:

   A 2D array with calibrated probabilities for each class, e.g. [[0.3, 0.7]] -> Option A

4. Quick Check:

   predict_proba output = 2D array [OK]

Hint: predict_proba always returns 2D array of class probabilities [OK]

Common Mistakes:

• Expecting a single float instead of array
• Confusing predict_proba with predict
• Misunderstanding cv='prefit' usage

4. You tried to calibrate a classifier using CalibratedClassifierCV with cv=5, but got an error: "ValueError: Expected cv split to be a cross-validation generator or an iterable, got int instead." What is the likely cause?

medium

A. You passed cv=5 but the dataset has fewer than 5 samples

B. You passed an integer instead of a cross-validation splitter object

C. You used an unsupported calibration method

D. You forgot to fit the base classifier before calibration

Solution

1. Step 1: Analyze the error message

   The error "Expected cv split to be a cross-validation generator or an iterable, got int instead." directly points to the cv parameter receiving an integer (5) where a splitter was expected.

2. Step 2: Check CalibratedClassifierCV cv usage

   This occurs when cv is passed as int but the context requires an explicit cross-validation object like StratifiedKFold(5).

3. Step 3: Rule out unrelated causes

   Base fitting (D) is for cv='prefit'; dataset size (B) or method (C) don't trigger this error.

4. Final Answer:

   You passed an integer instead of a cross-validation splitter object -> Option B

5. Quick Check:

   Error 'got int instead' = cv type mismatch [OK]

Hint: cv requires cross-validation generator or iterable, not plain int [OK]

Common Mistakes:

• Passing an integer to cv instead of a splitter object
• Confusing cv parameter usage
• Assuming calibration method causes error

5. You have a binary classifier that outputs probabilities but they are poorly calibrated. You want to improve calibration on a small dataset without losing model accuracy. Which approach is best?

hard

A. Discard probabilities and use only predicted labels

B. Retrain the model with more epochs to improve accuracy

C. Use isotonic regression calibration on a separate validation set

D. Apply Platt scaling calibration using cross-validation

Solution

1. Step 1: Consider calibration methods for small datasets

   Platt scaling (sigmoid) is preferred for small datasets because it is less prone to overfitting than isotonic regression.

2. Step 2: Use cross-validation to avoid losing accuracy

   Applying Platt scaling with cross-validation calibrates probabilities without retraining the base model or losing accuracy.

3. Step 3: Evaluate other options

   Isotonic regression may overfit small data, retraining may not fix calibration, discarding probabilities loses useful info.

4. Final Answer:

   Apply Platt scaling calibration using cross-validation -> Option D

5. Quick Check:

   Small data calibration = Platt scaling + CV [OK]

Hint: For small data, prefer Platt scaling with CV for calibration [OK]

Common Mistakes:

• Using isotonic regression on small data causing overfit
• Retraining model instead of calibrating
• Ignoring probability calibration importance