# MAPIE - Model Agnostic Prediction Interval Estimator¶

**MAPIE** allows you to easily estimate prediction intervals (or prediction sets)
using your favourite scikit-learn-compatible model for
single-output regression or multi-class classification settings.

Prediction intervals output by **MAPIE** encompass both aleatoric and epistemic
uncertainties and are backed by strong theoretical guarantees thanks to conformal
prediction methods [1-7].

# 🔗 Requirements¶

Python 3.7+

**MAPIE** stands on the shoulders of giants.

Its only internal dependencies are scikit-learn and numpy=>1.21.

# 🛠 Installation¶

Install via pip:

```
$ pip install mapie
```

or via conda:

```
$ conda install -c conda-forge mapie
```

To install directly from the github repository :

```
$ pip install git+https://github.com/scikit-learn-contrib/MAPIE
```

# ⚡️ Quickstart¶

Let us start with a basic regression problem. Here, we generate one-dimensional noisy data that we fit with a linear model.

```
import numpy as np
from sklearn.linear_model import LinearRegression
from sklearn.datasets import make_regression
regressor = LinearRegression()
X, y = make_regression(n_samples=500, n_features=1, noise=20, random_state=59)
```

Since MAPIE is compliant with the standard scikit-learn API, we follow the standard
sequential `fit`

and `predict`

process like any scikit-learn regressor.
We set two values for alpha to estimate prediction intervals at approximately one
and two standard deviations from the mean.

```
from mapie.regression import MapieRegressor
alpha = [0.05, 0.32]
mapie = MapieRegressor(regressor)
mapie.fit(X, y)
y_pred, y_pis = mapie.predict(X, alpha=alpha)
```

MAPIE returns a `np.ndarray`

of shape `(n_samples, 3, len(alpha))`

giving the predictions,
as well as the lower and upper bounds of the prediction intervals for the target quantile
for each desired alpha value.

You can compute the coverage of your prediction intervals.

```
from mapie.metrics import regression_coverage_score
coverage_scores = [
regression_coverage_score(y, y_pis[:, 0, i], y_pis[:, 1, i])
for i, _ in enumerate(alpha)
]
```

The estimated prediction intervals can then be plotted as follows.

```
from matplotlib import pyplot as plt
plt.xlabel("x")
plt.ylabel("y")
plt.scatter(X, y, alpha=0.3)
plt.plot(X, y_pred, color="C1")
order = np.argsort(X[:, 0])
plt.plot(X[order], y_pis[order][:, 0, 1], color="C1", ls="--")
plt.plot(X[order], y_pis[order][:, 1, 1], color="C1", ls="--")
plt.fill_between(
X[order].ravel(),
y_pis[order][:, 0, 0].ravel(),
y_pis[order][:, 1, 0].ravel(),
alpha=0.2
)
plt.title(
f"Target and effective coverages for "
f"alpha={alpha[0]:.2f}: ({1-alpha[0]:.3f}, {coverage_scores[0]:.3f})\n"
f"Target and effective coverages for "
f"alpha={alpha[1]:.2f}: ({1-alpha[1]:.3f}, {coverage_scores[1]:.3f})"
)
plt.show()
```

The title of the plot compares the target coverages with the effective coverages.
The target coverage, or the confidence interval, is the fraction of true labels lying in the
prediction intervals that we aim to obtain for a given dataset.
It is given by the alpha parameter defined in `MapieRegressor`

, here equal to 0.05 and 0.32,
thus giving target coverages of 0.95 and 0.68.
The effective coverage is the actual fraction of true labels lying in the prediction intervals.

# 📘 Documentation¶

The full documentation can be found on this link.

**How does MAPIE work?**

It is basically based on two types of techniques:

**Cross conformal predictions**

Conformity scores on the whole training set obtained by cross-validation,

Perturbed models generated during the cross-validation.

**MAPIE** then combines all these elements in a way that provides prediction intervals on new data with strong theoretical guarantees [1-2].

**Split conformal predictions**

Construction of a conformity score

Calibration of the conformity score on a calibration set not seen by the model during training

**MAPIE** then uses the calibrated conformity scores to estimate sets of labels associated with the desired coverage on new data with strong theoretical guarantees [3-4-5].

# 📝 Contributing¶

You are welcome to propose and contribute new ideas. We encourage you to open an issue so that we can align on the work to be done. It is generally a good idea to have a quick discussion before opening a pull request that is potentially out-of-scope. For more information on the contribution process, please go here.

# 🤝 Affiliations¶

MAPIE has been developed through a collaboration between Quantmetry, Michelin, ENS Paris-Saclay, and with the financial support from Région Ile de France and Confiance.ai.

# 🔍 References¶

MAPIE methods belong to the field of conformal inference.

[1] Rina Foygel Barber, Emmanuel J. Candès, Aaditya Ramdas, and Ryan J. Tibshirani. “Predictive inference with the jackknife+.” Ann. Statist., 49(1):486–507, February 2021.

[2] Byol Kim, Chen Xu, and Rina Foygel Barber. “Predictive Inference Is Free with the Jackknife+-after-Bootstrap.” 34th Conference on Neural Information Processing Systems (NeurIPS 2020).

[3] Mauricio Sadinle, Jing Lei, and Larry Wasserman. “Least Ambiguous Set-Valued Classifiers With Bounded Error Levels.” Journal of the American Statistical Association, 114:525, 223-234, 2019.

[4] Yaniv Romano, Matteo Sesia and Emmanuel J. Candès. “Classification with Valid and Adaptive Coverage.” NeurIPS 2020 (spotlight).

[5] Anastasios Nikolas Angelopoulos, Stephen Bates, Michael Jordan and Jitendra Malik. “Uncertainty Sets for Image Classifiers using Conformal Prediction.” International Conference on Learning Representations 2021.

[6] Yaniv Romano, Evan Patterson, Emmanuel J. Candès. “Conformalized Quantile Regression.” Advances in neural information processing systems 32 (2019).

[7] Chen Xu and Yao Xie. “Conformal Prediction Interval for Dynamic Time-Series.” International Conference on Machine Learning (ICML, 2021).

[8] Lihua Lei Jitendra Malik Stephen Bates, Anastasios Angelopoulos and Michael I. Jordan. Distribution-free, risk-controlling prediction sets. CoRR, abs/2101.02703, 2021. URL https://arxiv.org/abs/2101.02703.39

[9] Angelopoulos, Anastasios N., Stephen, Bates, Adam, Fisch, Lihua, Lei, and Tal, Schuster. “Conformal Risk Control.” (2022).

# 📝 License¶

MAPIE is free and open-source software licensed under the 3-clause BSD license.