crepes.py

It’s clear that the **`crepes`** package provides a flexible and powerful framework for conformal prediction, particularly with the ability to integrate classifiers and calibrate predictions. Considering the challenges with previous approaches (e.g., MAPIE), **`crepes`** appears to be a promising alternative to achieve the desired goals of calibrated probabilities and valid prediction sets.

Let’s break down how we can approach integrating **`crepes`** into your existing pipeline and possibly retain aspects like **beta calibration**:

---

### **Goals to Achieve:**
1. Use the best pre-trained **CatBoost model** (with optimal hyperparameters and selected features) as the base model.
2. Integrate **beta calibration** for probability calibration if applicable.
3. Leverage **`crepes.WrapClassifier`** for conformal prediction, producing **calibrated probabilities** and **prediction sets**.
4. Evaluate the results with metrics like:
   - Coverage (proportion of true labels within prediction sets).
   - Interval width (size of prediction sets).

---

### **Steps to Implement Conformal Prediction with `crepes`**

#### **1. Wrap the Pre-Trained CatBoost Model**
The **`WrapClassifier`** in `crepes` can handle any scikit-learn-compatible classifier, including your pre-trained CatBoost model. Here’s how to integrate it:

```python
from crepes import WrapClassifier

# Assuming `model` is your pre-trained CatBoostClassifier
wrapped_model = WrapClassifier(model)

# Display the wrapped model
display(wrapped_model)
```

#### **2. Calibrate the Model**
Use the calibration dataset (`X_calib_selected` and `y_calib`) to calibrate the wrapped model.

```python
# Calibrate the model using the calibration dataset
wrapped_model.calibrate(X_calib_selected, y_calib)

# Check calibration status
display(wrapped_model)
```

#### **3. Generate Prediction Sets**
Once calibrated, you can generate prediction sets for the test dataset (`X_test_selected`) using `predict_set`. For example, a 95% confidence level:

```python
# Generate prediction sets for 95% confidence level
prediction_sets = wrapped_model.predict_set(X_test_selected, confidence=0.95)

# Display the prediction sets (binary arrays for each class)
print(prediction_sets)
```

#### **4. Generate Calibrated Probabilities**
To retrieve calibrated probabilities, you can use `predict_proba` on the wrapped model:

```python
# Get calibrated probabilities
calibrated_probs = wrapped_model.predict_proba(X_test_selected)

# Display calibrated probabilities
print(calibrated_probs)
```

#### **5. Evaluate the Model**
Use the `evaluate` method to assess performance, such as coverage and error rates:

```python
# Evaluate performance at a 95% confidence level
evaluation_results = wrapped_model.evaluate(X_test_selected, y_test, confidence=0.95)

# Display evaluation results
print(evaluation_results)
```

---

### **Considerations for Beta Calibration**
If beta calibration was highly effective for your use case, you might want to **pre-calibrate probabilities** using beta calibration and then pass these probabilities to `crepes` for conformal prediction. Here’s how:

1. **Apply Beta Calibration:**
   Calibrate the model’s predicted probabilities with beta calibration before wrapping it with `crepes`.

   ```python
   # Calibrate probabilities with beta calibration
   calibrated_probs = beta_calibrator.predict_proba(model.predict_proba(X_calib_selected)[:, 1].reshape(-1, 1))
   ```

2. **Pass Pre-Calibrated Probabilities to `WrapClassifier`:**
   Modify the `WrapClassifier` or use `crepes`' internal classes like `ConformalClassifier` to handle pre-calibrated probabilities.

---

### **Visualization of Results**
Once you have the calibrated probabilities and prediction sets, you can visualize the results:

1. **Plot Prediction Sets:**
   ```python
   import matplotlib.pyplot as plt

   plt.figure(figsize=(10, 6))
   for i, pred_set in enumerate(prediction_sets[:100]):  # Plot first 100 samples
       plt.scatter([i] * len(pred_set), pred_set, color="blue")
   plt.title("Prediction Sets for First 100 Samples")
   plt.xlabel("Sample Index")
   plt.ylabel("Prediction Set")
   plt.show()
   ```

2. **Compare Coverage:**
   Evaluate how often the true label falls within the prediction sets.

---

### **Next Steps**
1. **Implement the steps above with `crepes`.**
2. **Decide whether to retain beta calibration or switch entirely to `crepes`.**
   - If retaining beta calibration, we’ll need to pass pre-calibrated probabilities to `crepes`.
3. **Visualize results and evaluate metrics.**

Would you like me to assist further with a specific implementation step or troubleshoot any part of this process?