带Reject Option的机器学习技术问询：思路、工具与阈值选择

Great question! Reject options are super useful when dealing with ambiguous samples where you don’t want your model to guess blindly—let’s break this down into actionable parts:

There are two main schools of thought when implementing a reject option:

1. Modular "Classify-Then-Reject" Pipeline #

This is the most common, straightforward approach:

• Confidence-Based Rejection: Train a standard classifier first, then reject samples where the model's highest predicted class probability falls below a set threshold. This relies on having reliable, calibrated probability outputs.
• Distance-Based Rejection: For models like SVMs or k-NN, reject samples that sit close to decision boundaries (low margin) or fall outside the model's "certainty region" (e.g., samples far from all training points in k-NN).

2. End-to-End Reject Learning #

Integrate rejection directly into the model's training loop to optimize for both classification and rejection performance:

• Add a "Reject" Class: Treat rejection as an explicit class in your dataset. The model learns to predict either a normal class or the reject class, just like a multi-class task.
• Custom Loss Functions: Modify your loss to penalize incorrect predictions more heavily than rejection. For example, if the model is uncertain, choosing to reject incurs a small fixed loss instead of a large misclassification loss.

While there aren’t many dedicated "reject option" libraries, most popular ML frameworks make implementation easy:

• scikit-learn:
  • Use CalibratedClassifierCV to calibrate your model’s predicted probabilities (critical for reliable confidence-based rejection).
  • Pair any classifier with custom rejection logic using predict_proba (see example code below).
• TensorFlow/PyTorch:
  • Build end-to-end reject models by adding a reject class to your output layer, or write a custom loss function that includes rejection penalties.
• Creme: This online learning library has built-in support for reject options in some classifiers (e.g., creme.tree.HoeffdingTreeClassifier includes a reject_threshold parameter).

Quick scikit-learn Implementation Example #

from sklearn.datasets import load_iris
from sklearn.ensemble import RandomForestClassifier
from sklearn.calibration import CalibratedClassifierCV
from sklearn.model_selection import train_test_split

# Load and split dataset
X, y = load_iris(return_X_y=True)
X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=42)

# Train a calibrated classifier (for trustworthy probability scores)
base_clf = RandomForestClassifier(random_state=42)
calibrated_clf = CalibratedClassifierCV(base_clf, cv=5, method='sigmoid')
calibrated_clf.fit(X_train, y_train)

# Define prediction function with rejection logic
def predict_with_reject(X, threshold=0.8):
    probs = calibrated_clf.predict_proba(X)
    max_confidence = probs.max(axis=1)
    preds = calibrated_clf.predict(X)
    # Mark low-confidence samples as rejected (-1)
    preds[max_confidence < threshold] = -1
    return preds

The optimal threshold depends on your tradeoff between classification accuracy and rejection rate, plus the real-world costs of errors vs. rejection. Here are practical methods:

1. Expected Loss Minimization #

Define two clear costs:

• C_err: Cost of a wrong classification (e.g., $100 for a misdiagnosis)
• C_rej: Cost of rejecting a sample (e.g., $20 for manual review)

Reject a sample if (1 - max_prob) * C_err > C_rej—this ensures the cost of guessing incorrectly outweighs the cost of rejection.

2. Accuracy-Rejection Rate Tradeoff #

Plot a curve of validation set accuracy against rejection rate as you adjust the threshold. Pick the point that aligns with your business needs—for example, if you can tolerate a 10% rejection rate to hit 98% accuracy, select the threshold that achieves this balance.

3. Quantile-Based Thresholding #

Use your validation set's confidence scores to set a threshold based on a quantile. For example, if you want to reject the 10% least confident samples, sort the validation set's maximum probabilities and use the 10th percentile as your threshold.

4. Adaptive Thresholding #

For dynamic environments (e.g., streaming data), update the threshold over time using recent samples. Use a sliding window to recalculate the threshold based on current model performance and data distribution shifts.

Critical Note #

Always calibrate your model’s probabilities first! Uncalibrated scores (like raw outputs from SVMs or uncalibrated tree models) will lead to unreliable rejection decisions.

内容的提问来源于stack exchange，提问作者Gloria