Binary Classifier Calibration using an Ensemble of Near Isotonic Regression Models

Learning accurate probabilistic models from data is crucial in many practical tasks in data mining. In this paper we present a new non-parametric calibration method called \textit{ensemble of near isotonic regression} (ENIR). The method can be considered as an extension of BBQ, a recently proposed calibration method, as well as the commonly used calibration method based on isotonic regression. ENIR is designed to address the key limitation of isotonic regression which is the monotonicity assumption of the predictions. Similar to BBQ, the method post-processes the output of a binary classifier to obtain calibrated probabilities. Thus it can be combined with many existing classification models. We demonstrate the performance of ENIR on synthetic and real datasets for the commonly used binary classification models. Experimental results show that the method outperforms several common binary classifier calibration methods. In particular on the real data, ENIR commonly performs statistically significantly better than the other methods, and never worse. It is able to improve the calibration power of classifiers, while retaining their discrimination power. The method is also computationally tractable for large scale datasets, as it is $O(N \log N)$ time, where $N$ is the number of samples

Calculating classifier calibration performance with a custom modification of Weka

Calibration is often overlooked in machine-learning problem-solving approaches, even in situations where an accurate estimation of predicted probabilities, and not only a discrimination between classes, is critical for decision-making. One of the reasons is the lack of readily available open-source software packages which can easily calculate calibration metrics. In order to provide one such tool, we have developed a custom modification of the Weka data mining software, which implements the calculation of Hosmer-Lemeshow groups of risk and the Pearson chi-square statistic comparison between estimated and observed frequencies for binary problems. We provide calibration performance estimations with Logistic regression (LR), BayesNet, Naïve Bayes, artificial neural network (ANN), support vector machine (SVM), knearest neighbors (KNN), decision trees and Repeated Incremental Pruning to Produce Error Reduction (RIPPER) models with six different datasets. Our experiments show that SVMs with RBF kernels exhibit the best results in terms of calibration, while decision trees, RIPPER and KNN are highly unlikely to produce well-calibrated models

OBTAINING ACCURATE PROBABILITIES USING CLASSIFIER CALIBRATION

Learning probabilistic classification and prediction models that generate accurate probabilities is essential in many prediction and decision-making tasks in machine learning and data mining. One way to achieve this goal is to post-process the output of classification models to obtain more accurate probabilities. These post-processing methods are often referred to as calibration methods in the machine learning literature. This thesis describes a suite of parametric and non-parametric methods for calibrating the output of classification and prediction models. In order to evaluate the calibration performance of a classifier, we introduce two new calibration measures that are intuitive statistics of the calibration curves. We present extensive experimental results on both simulated and real datasets to evaluate the performance of the proposed methods compared with commonly used calibration methods in the literature. In particular, in terms of binary classifier calibration, our experimental results show that the proposed methods are able to improve the calibration power of classifiers while retaining their discrimination performance. Our theoretical findings show that by using a simple non-parametric calibration method, it is possible to improve the calibration performance of a classifier without sacrificing discrimination capability. The methods are also computationally tractable for large-scale datasets as they run in O(N log N) time, where N is the number of samples. In this thesis we also introduce a novel framework to derive calibrated probabilities of causal relationships from observational data. The framework consists of three main components: (1) an approximate method for generating initial probability estimates of the edge types for each pair of variables, (2) the availability of a relatively small number of the causal relationships in the network for which the truth status is known, which we call a calibration training set, and (3) a calibration method for using the approximate probability estimates and the calibration training set to generate calibrated probabilities for the many remaining pairs of variables. Our experiments on a range of simulated data support that the proposed approach improves the calibration of edge predictions. The results also support that the approach often improves the precision and recall of those predictions