Probmetrics: Classification metrics and post-hoc calibration

This package (PyTorch-based) currently contains

• classification metrics, especially also metrics for assessing the quality of probabilistic predictions, and
• post-hoc calibration methods, especially
  • a fast and accurate implementation of temperature scaling.
  • an implementation of structured matrix scaling (SMS), a regularized version of matrix scaling that outperforms other logistic-based calibration functions.

It accompanies our papers Rethinking Early Stopping: Refine, Then Calibrate and Structured Matrix Scaling for Multi-Class Calibration and A Variational Estimator for Lp Calibration Errors. Please cite us if you use this repository for research purposes. The experiments from the papers can be found here:

• Rethinking Early Stopping:
  • vision experiments.
  • tabular experiments.
  • theory.
• Structured Matrix Scaling: all experiments.
• A Variational Estimator for Lp Calibration Errors: all experiments.

Installation

Probmetrics is available via

pip install probmetrics

To obtain all functionality, install probmetrics[extra,dev,dirichletcal].

• extra installs more packages for our CatBoost/LightGBM-based $L_p$ calibration error metrics, smooth ECE (only works with scikit-learn versions <= 1.6), Venn-Abers calibration, centered isotonic regression, and the temperature scaling implementation in NetCal.
• dev installs more packages for development (esp. testing)
• dirichletcal installs Dirichlet calibration, which however only works for Python 3.12 upwards.

Using post-hoc calibration methods

You can create a calibrator as follows:

from probmetrics.calibrators import get_calibrator

calib = get_calibrator('logistic')

These are the main supported methods:

• 'logistic' defaults to structured matrix scaling (SMS) for multiclass and quadratic scaling for binary calibration. We recommend using 'logistic' for best results, especially on multiclass problems. It can be slow for larger numbers of classes. Only runs on CPU. For the SAGA version (not the default), the first call is slower due to numba compilation.
• 'svs': Structured vector scaling (SVS) for multiclass problems, faster than SMS for multiclass while being almost as good in many cases.
• 'affine-scaling': Affine scaling for binary problems, underperforms 'logistic' (quadratic scaling) in our benchmarks but preserves AUC.
• 'temp-scaling': Our highly efficient implementation of temperature scaling that, unlike some other implementations, does not suffer from optimization issues. Temperature scaling is not as expressive as matrix or vector scaling variants, but it is faster and has the least overfitting risk.
• 'ts-mix': Same as 'temp-scaling' but with Laplace smoothing (slightly preferable for logloss). Can also be achieved using get_calibrator('temp-scaling', calibrate_with_mixture=True)
• 'isotonic' Isotonic regression from scikit-learn. Isotonic variants can be good for binary classification with enough data (around 10K samples or more)
• 'ivap' Inductive Venn-Abers predictor (a version of isotonic regression, slow but a bit better)
• 'cir' Centered isotonic regression (slightly better and slower than isotonic)
• 'dircal' Dirichlet calibration (slow, logistic performs better in our experiments)
• 'dircal-cv' Dirichlet calibration optimized with cross-validation (very slow)

More details on parameters and other methods can be found in the get_calibrator function here.

Usage with numpy

import numpy as np

probas = np.asarray([[0.1, 0.9]])  # shape = (n_samples, n_classes)
labels = np.asarray([1])  # shape = (n_samples,)
calib.fit(probas, labels)
calibrated_probas = calib.predict_proba(probas)

Usage with PyTorch

The PyTorch version can be used directly with GPU tensors, which is leveraged by our temperature scaling implementation but not by most other methods. For temperature scaling, this could accelerate things, but the CPU version can be faster for smaller validation sets (around 1K-10K samples).

from probmetrics.distributions import CategoricalProbs
import torch

probas = torch.as_tensor([[0.1, 0.9]])
labels = torch.as_tensor([1])

# if you have logits, you can use CategoricalLogits instead
calib.fit_torch(CategoricalProbs(probas), labels)
result = calib.predict_proba_torch(CategoricalProbs(probas))
calibrated_probas = result.get_probs()

Using our refinement and calibration metrics

We provide estimators for refinement error (loss after post-hoc calibration) and calibration error (loss improvement through post-hoc calibration). They can be used as follows:

import torch
from probmetrics.metrics import Metrics

# compute multiple metrics at once 
# this is more efficient than computing them individually
metrics = Metrics.from_names(['logloss', 
                              'refinement_logloss_ts-mix_all', 
                              'calib-err_logloss_ts-mix_all'])
y_true = torch.tensor(...)
y_logits = torch.tensor(...)
results = metrics.compute_all_from_labels_logits(y_true, y_logits)
print(results['refinement_logloss_ts-mix_all'].item())

Using more metrics

In general, while some metrics can be flexibly configured using the corresponding classes, many metrics are available through their name. Here are some relevant classification metrics:

from probmetrics.metrics import Metrics

metrics = Metrics.from_names([
    'logloss',
    'brier',  # for binary, this is 2x the brier from sklearn
    'accuracy', 'class-error',
    'auroc-ovr', # one-vs-rest
    'auroc-ovo-sklearn', # one-vs-one (can be slow!)
    # calibration metrics
    'ece-15', 'rmsce-15', 'mce-15', 'smece'
    'refinement_logloss_ts-mix_all', 
    'calib-err_logloss_ts-mix_all',
    'refinement_brier_ts-mix_all', 
    'calib-err_brier_ts-mix_all',
    'calib-err_proper-L1-binary-as-1d_WS_CatboostClassifier_all',
    'calib-err_proper-L2-binary-as-1d_WS_CatboostClassifier_all',
    'calib-err_proper-Linf-binary-as-1d_WS_CatboostClassifier_all',
])

The following function returns a list of all metric names:

from probmetrics.metrics import Metrics, MetricType
Metrics.get_available_names(metric_type=MetricType.CLASS)

While there are some classes for regression metrics, they are not implemented.

Advanced calibration, confidence, and top-class metrics

Beyond standard metrics, you can evaluate proper Lp calibration errors for any p, as well as isolate specific types of errors like over-confidence, under-confidence, and top-class errors.

Note: Over- and under-confidence metrics are designed for binary classification. To use those for multi-class, please use TopClassLoss(OverConfidenceLoss(your_metric)).

from probmetrics.metrics import (
  ProperLpLoss,
  BrierLoss,
  OverConfidenceLoss,
  UnderConfidenceLoss,
  TopClassLoss
)

# Evaluate proper Lp calibration errors for any p
lp_loss_l1 = ProperLpLoss(p=1)  # Evaluate E[ \| Y - E[Y|f(X)] \|_1 ] 
lp_loss_l2 = ProperLpLoss(p=2)  # Evaluate E[ \| Y - E[Y|f(X)] \|_2 ] 

# Evaluate over-confidence and under-confidence 
# (Initialize via string name or by passing a metric object)
over_brier = OverConfidenceLoss.from_name("brier")
under_L1 = UnderConfidenceLoss.from_name("proper-L1")

# Evaluate top-class error with any accompanying loss
topclass_brier = TopClassLoss(BrierLoss(binary_as_multiclass=False))
topclass_L1 = TopClassLoss.from_name("proper-L1")

# Compose wrappers (e.g., top-class with underconfidence for proper-L1)
under_topclass_l1 = TopClassLoss(UnderConfidenceLoss.from_name("proper-L1"))
over_topclass_brier = TopClassLoss(OverConfidenceLoss(BrierLoss()))

# Some metrics are listed by default, here are some of them
metrics = metrics = Metrics.from_names([
    'proper-L1-binary-as-1d', # use to estimate  E[ \| Y - E[Y|f(X)] \|_1 ] and treat binary 
                              # predictions as scalars with shapes (n,1) )
    'proper-L2', # use to estimate  E[ \| Y - E[Y|f(X)] \|_2 ] (and treat binary predictions 
                 # as vector with shapes (n,2) )
    "topclass-proper-L1-binary-as-1d", # Estimate L1 calibration error of top class 
    "topclass-under-proper-L1-binary-as-1d", # Estimate L1-overconfidence of top class 
    "topclass-over-proper-L1-binary-as-1d", # Estimate L1-underconfidence of top class
])

Once those losses are defined, you can evaluate the calibration error by doing:

from probmetrics.metrics import MetricsWithCalibration, CombinedMetrics
from probmetrics.classifiers import WS_CatboostClassifier, WS_LGBMClassifier
from probmetrics.splitters import CVSplitter

loss = ProperLpLoss(p=2) 

metrics = MetricsWithCalibration(loss,
                            calibrator=WS_CatboostClassifier(), # The classifier used to recalibrate the predictions
                            val_splitter=CVSplitter(n_cv=5) # cross-validation splitter
                            )

# or use combined metrics to evaluate multiple metrics 
# while fitting the post-hoc calibrator only once
combined_losses = CombinedMetrics( 
                                    [
                                    ProperLpLoss(p=1), 
                                    OverConfidenceLoss.from_name("brier"), 
                                    OverConfidenceLoss.from_name("proper-L1") , 
                                    UnderConfidenceLoss.from_name("proper-L1" ), 
                                    UnderConfidenceLoss( BrierLoss() ),
                                    BrierLoss()
                                    ]
                                  )

metrics = MetricsWithCalibration(combined_losses,
                            calibrator=WS_LGBMClassifier(), 
                            val_splitter=CVSplitter(n_cv=5)
                            )

y_true = torch.tensor(...)
y_prob = torch.tensor(...)
results = metrics.compute_all_from_labels_probs(y_true, y_prob)

The calibrator argument is a class used to recalibrate the original predictions. Any estimator that inherits from sklearn.base.ClassifierMixin (i.e., follows the scikit-learn classifier API) and implements predict_proba() can be used. We recommend using WS_CatboostClassifier with default parameters. The "WS" stands for "Warm Start", as predictions are initialized at the original predicted $f(x)$ values (see the paper A Variational Estimator for Lp Calibration Errors for additional information).

Binary vs. multiclass formatting

The library internally stores predictions in a multiclass format with shape (n_samples, n_classes). For binary classification, for some metrics you can control whether to treat the output as a two-column distribution or a single-column probability using the binary_as_multiclass parameter. For example, for BrierLoss(), using binary_as_multiclass=False will yield the scikit-learn formula, while binary_as_multiclass=True will yield twice the value.

Setting binary_as_multiclass=False tells the loss function to treat (n_samples, 2) predictions as a single-column (n_samples, 1) probability. The loss then internally transforms the data to binary labels $Y \in {0, 1}$ and the probability column $f(X) \in [0, 1]$ for the calculation.

Those features are also valid with the TopClassLoss. The TopClassLoss wrapper focuses the loss calculation on the class with the highest predicted probability. The behavior changes based on your binary setting, for instance:

Configuration	Estimate	Description
TopClassLoss(ProperLpLoss(p=1))	$\mathbb{E}[ \lvert Z - \mathbb{E}[Z \mid \max f(X)] \rvert ]$	Scalar probability: $\max f(X)$ is the scalar probability of the top class of $f(X)$; $Z \in {0, 1}$ equals $1$ if the label is what the top-class predicted and $0$ otherwise. Evaluates the absolute error of the top-class prediction.
TopClassLoss(ProperLpLoss(p=1, binary_as_multiclass=True))	$\mathbb{E}[ \Vert \mathbf{Z} - \mathbb{E}[\mathbf{Z} \mid \max f(X)] \Vert_1 ]$	Vectorized: $\mathbf{Z}$ is a one-hot vector. Calculates the $L_1$ norm of the error vector.

When used inside MetricsWithCalibration, TopClassLoss will choose the top-class based on $f(X)$ instead of $g(f(X))$ so the loss difference uses the same choice of top class for both terms.

Contributors

• David Holzmüller
• Eugène Berta
• Sacha Braun

Releases

• v1.2.0 by @elsacho: Added new proper loss functions:
  • ProperLpLoss(p=p): Metrics to evaluate $E[ \Vert f(X) - E[Y|f(X)] \Vert_p ]$ where $f(X)$ are the predictions of the classifier, $p &gt;= 1$, including p=float("inf")
  • TopClassLoss: A wrapper to variationally evaluate top-class errors.
  • OverConfidenceLoss & UnderConfidenceLoss: Wrappers to variationally evaluate over/under-confidence in binary predictors.
  • MetricsWithCalibration can now handle arbitrary classifiers and Lp-type losses.
  • New classifiers: Added WS_CatboostClassifier and WS_LGBMClassifier for evaluating calibration errors.
  • removed sklearn < 1.7 constraint.
• v1.1.0 by @eugeneberta: Improvements to the SVS and SMS calibrators:
  • logit pre-processing with 'ts-mix' is now automatic, and the global scaling parameter $\alpha$ is fixed to 1. This yields:
    • improved performance on our tabular and computer vision benchmarks (see the arxiv v2 of the SMS paper, coming soon).
    • faster convergence.
    • ability to compute the duality gap in closed form for stopping SAGA solvers, which we implement in this version.
  • improved L-BFGS solvers, much faster than in the previous version. Now used in SVS and SMS by default.
  • the default binary calibrator in LogisticCalibrator is now quadratic scaling instead of affine scaling, this can be changed back by using LogisticCalibrator(binary_type='affine').
• v1.0.0 by @eugeneberta: New post-hoc calibrators like 'logistic' including structured matrix scaling (SMS), structured vector scaling (SVS), affine scaling, and quadratic scaling.
• v0.0.2 by @dholzmueller:
  • Removed numpy<2.0 constraint
  • allow 1D vectors in CategoricalLogits / CategoricalProbs
  • add TorchCal temperature scaling
  • minor fixes in AutoGluon temperature scaling that shouldn't affect the performance in practice
• v0.0.1 by @dholzmueller: Initial release with classification metrics, calibration/refinement metrics, and some post-hoc calibration methods.