Classifier Calibration

HiClass provides support for probability calibration using various post-hoc calibration methods.

Motivation

While many machine learning models can output uncertainty scores, these scores are known to be often poorly calibrated 1 2. Model calibration aims to improve the quality of probabilistic forecasts by learning a transformation of the scores, using a separate dataset.

Methods

HiClass supports the following calibration methods:

Isotonic Regression 3
Platt Scaling 4
Beta Calibration 5
Inductive Venn-Abers Calibration 6
Cross Venn-Abers Calibration 6

Probability Aggregation

Combining probabilities over multiple levels is another method to improve probabilistic forecasts. The following methods are supported:

Conditional Probability Aggregation (Multiply Aggregation)

Given a node hierarchy with \(n\) levels, the probability of a node \(A_i\), where \(i\) denotes the level, is calculated as:

\(\displaystyle{\mathbb{P}(A_1 \cap A_2 \cap \ldots \cap A_i) = \mathbb{P}(A_1) \cdot \mathbb{P}(A_2 \mid A_1) \cdot \mathbb{P}(A_3 \mid A_1 \cap A_2) \cdot \ldots}\) \(\displaystyle{\cdot \mathbb{P}(A_i \mid A_1 \cap A_2 \cap \ldots \cap A_{i-1})}\)

Arithmetic Mean Aggregation

\(\displaystyle{\mathbb{P}(A_i) = \frac{1}{i} \sum_{j=1}^{i} \mathbb{P}(A_{j})}\)

Geometric Mean Aggregation

\(\displaystyle{\mathbb{P}(A_i) = \exp{\left(\frac{1}{i} \sum_{j=1}^{i} \ln \mathbb{P}(A_{j})\right)}}\)

Code sample

from sklearn.ensemble import RandomForestClassifier

from hiclass import LocalClassifierPerNode

# Define data
X_train = [[1], [2], [3], [4]]
X_test = [[4], [3], [2], [1]]
X_cal = [[5], [6], [7], [8]]
Y_train = [
    ["Animal", "Mammal", "Sheep"],
    ["Animal", "Mammal", "Cow"],
    ["Animal", "Reptile", "Snake"],
    ["Animal", "Reptile", "Lizard"],
]

Y_cal = [
    ["Animal", "Mammal", "Cow"],
    ["Animal", "Mammal", "Sheep"],
    ["Animal", "Reptile", "Lizard"],
    ["Animal", "Reptile", "Snake"],
]

# Use random forest classifiers for every node
rf = RandomForestClassifier()

# Use local classifier per node with isotonic regression as calibration method
classifier = LocalClassifierPerNode(
    local_classifier=rf, calibration_method="isotonic", probability_combiner="multiply"
)

# Train local classifier per node
classifier.fit(X_train, Y_train)

# Calibrate local classifier per node
classifier.calibrate(X_cal, Y_cal)

# Predict probabilities
probabilities = classifier.predict_proba(X_test)

# Print probabilities and labels for the last level
print(classifier.classes_[2])
print(probabilities)

1: Niculescu-Mizil, Alexandru; Caruana, Rich (2005): Predicting good probabilities with supervised learning. In: Saso Dzeroski (Hg.): Proceedings of the 22nd international conference on Machine learning - ICML ‘05. the 22nd international conference. Bonn, Germany, 07.08.2005 - 11.08.2005. New York, New York, USA: ACM Press, S. 625-632.
2: Chuan Guo; Geoff Pleiss; Yu Sun; Kilian Q. Weinberger (2017): On Calibration of Modern Neural Networks. In: Doina Precup und Yee Whye Teh (Hg.): Proceedings of the 34th International Conference on Machine Learning, Bd. 70: PMLR (Proceedings of Machine Learning Research), S. 1321-1330.
3: Zadrozny, Bianca; Elkan, Charles (2002): Transforming classifier scores into accurate multiclass probability estimates. In: Proceedings of the Eighth ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York, NY, USA: Association for Computing Machinery (KDD ’02), S. 694-699.
4: Platt, John (2000): Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods. In: Adv. Large Margin Classif. 10.
5: Kull, Meelis; Filho, Telmo Silva; Flach, Peter (2017): Beta calibration: a well-founded and easily implemented improvement on logistic calibration for binary classifiers. In: Aarti Singh und Jerry Zhu (Hg.): Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, Bd. 54: PMLR (Proceedings of Machine Learning Research), S. 623-631.
6(1,2): Vovk, Vladimir; Petej, Ivan; Fedorova, Valentina (2015): Large-scale probabilistic predictors with and without guarantees of validity. In: C. Cortes, N. Lawrence, D. Lee, M. Sugiyama und R. Garnett (Hg.): Advances in Neural Information Processing Systems, Bd. 28: Curran Associates, Inc.