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

A Comparative Analysis of Ensemble Classifiers: Case Studies in Genomics

The combination of multiple classifiers using ensemble methods is increasingly important for making progress in a variety of difficult prediction problems. We present a comparative analysis of several ensemble methods through two case studies in genomics, namely the prediction of genetic interactions and protein functions, to demonstrate their efficacy on real-world datasets and draw useful conclusions about their behavior. These methods include simple aggregation, meta-learning, cluster-based meta-learning, and ensemble selection using heterogeneous classifiers trained on resampled data to improve the diversity of their predictions. We present a detailed analysis of these methods across 4 genomics datasets and find the best of these methods offer statistically significant improvements over the state of the art in their respective domains. In addition, we establish a novel connection between ensemble selection and meta-learning, demonstrating how both of these disparate methods establish a balance between ensemble diversity and performance.Comment: 10 pages, 3 figures, 8 tables, to appear in Proceedings of the 2013 International Conference on Data Minin

Sequential Linearithmic Time Optimal Unimodal Fitting When Minimizing Univariate Linear Losses

This paper focuses on optimal unimodal transformation of the score outputs of a univariate learning model under linear loss functions. We demonstrate that the optimal mapping between score values and the target region is a rectangular function. To produce this optimal rectangular fit for the observed samples, we propose a sequential approach that can its estimation with each incoming new sample. Our approach has logarithmic time complexity per iteration and is optimally efficient.Comment: this work draws from arXiv:2108.0878

An experimental investigation of calibration techniques for imbalanced data

Calibration is a technique used to obtain accurate probability estimation for classification problems in real applications. Class imbalance can create considerable challenges in obtaining accurate probabilities for calibration methods. However, previous research has paid little attention to this issue. In this paper, we present an experimental investigation of some prevailing calibration methods in different imbalance scenarios. Several performance metrics are considered to evaluate different aspects of calibration performance. The experimental results show that the performance of different calibration techniques depends on the metrics and the degree of the imbalance ratio. Isotonic Regression has better overall performance on imbalanced datasets than parametric and other complex non-parametric methods. However, it performs unstably in highly imbalanced scenarios. This study provides some insights into calibration methods on imbalanced datasets, and it can be a reference for the future development of calibration methods in class imbalance scenarios

Classifier Subset Selection to construct multi-classifiers by means of estimation of distribution algorithms

This paper proposes a novel approach to select the individual classifiers to take part in a Multiple-Classifier System. Individual classifier selection is a key step in the development of multi-classifiers. Several works have shown the benefits of fusing complementary classifiers. Nevertheless, the selection of the base classifiers to be used is still an open question, and different approaches have been proposed in the literature. This work is based on the selection of the appropriate single classifiers by means of an evolutionary algorithm. Different base classifiers, which have been chosen from different classifier families, are used as candidates in order to obtain variability in the classifications given. Experimental results carried out with 20 databases from the UCI Repository show how adequate the proposed approach is; Stacked Generalization multi-classifier has been selected to perform the experimental comparisons.The work described in this paper was partially conducted within the Basque Government Research Team grant and the University of the Basque Country UPV/EHU and under grant UFI11/45 (BAILab)

Setting decision thresholds when operating conditions are uncertain

[EN] The quality of the decisions made by a machine learning model depends on the data and the operating conditions during deployment. Often, operating conditions such as class distribution and misclassification costs have changed during the time since the model was trained and evaluated. When deploying a binary classifier that outputs scores, once we know the new class distribution and the new cost ratio between false positives and false negatives, there are several methods in the literature to help us choose an appropriate threshold for the classifier's scores. However, on many occasions, the information that we have about this operating condition is uncertain. Previous work has considered ranges or distributions of operating conditions during deployment, with expected costs being calculated for ranges or intervals, but still the decision for each point is made as if the operating condition were certain. The implications of this assumption have received limited attention: a threshold choice that is best suited without uncertainty may be suboptimal under uncertainty. In this paper we analyse the effect of operating condition uncertainty on the expected loss for different threshold choice methods, both theoretically and experimentally. We model uncertainty as a second conditional distribution over the actual operation condition and study it theoretically in such a way that minimum and maximum uncertainty are both seen as special cases of this general formulation. This is complemented by a thorough experimental analysis investigating how different learning algorithms behave for a range of datasets according to the threshold choice method and the uncertainty level.We thank the anonymous reviewers for their comments, which have helped to improve this paper significantly. This work has been partially supported by the EU (FEDER) and the Spanish MINECO under Grant TIN 2015-69175-C4-1-R and by Generalitat Valenciana under Grant PROMETEOII/2015/013. Jose Hernandez-Orallo was supported by a Salvador de Madariaga Grant (PRX17/00467) from the Spanish MECD for a research stay at the Leverhulme Centre for the Future of Intelligence (CFI), Cambridge, a BEST Grant (BEST/2017/045) from Generalitat Valenciana for another research stay also at the CFI and an FLI Grant RFP2-152.Ferri Ramírez, C.; Hernández-Orallo, J.; Flach, P. (2019). Setting decision thresholds when operating conditions are uncertain. Data Mining and Knowledge Discovery. 33(4):805-847. https://doi.org/10.1007/s10618-019-00613-7S805847334Adams N, Hand D (1999) Comparing classifiers when the misallocation costs are uncertain. Pattern Recognit 32(7):1139–1147Bella A, Ferri C, Hernández-Orallo J, Ramírez-Quintana MJ (2013) On the effect of calibration in classifier combination. 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Aggregative quantification for regression

The final publication is available at Springer via http://dx.doi.org/10.1007/s10618-013-0308-zThe problem of estimating the class distribution (or prevalence) for a new unlabelled dataset (from a possibly different distribution) is a very common problem which has been addressed in one way or another in the past decades. This problem has been recently reconsidered as a new task in data mining, renamed quantification when the estimation is performed as an aggregation (and possible adjustment) of a single-instance supervised model (e.g., a classifier). However, the study of quantification has been limited to classification, while it is clear that this problem also appears, perhaps even more frequently, with other predictive problems, such as regression. In this case, the goal is to determine a distribution or an aggregated indicator of the output variable for a new unlabelled dataset. In this paper, we introduce a comprehensive new taxonomy of quantification tasks, distinguishing between the estimation of the whole distribution and the estimation of some indicators (summary statistics), for both classification and regression. This distinction is especially useful for regression, since predictions are numerical values that can be aggregated in many different ways, as in multi-dimensional hierarchical data warehouses. We focus on aggregative quantification for regression and see that the approaches borrowed from classification do not work. We present several techniques based on segmentation which are able to produce accurate estimations of the expected value and the distribution of the output variable. We show experimentally that these methods especially excel for the relevant scenarios where training and test distributions dramatically differ.We would like to thank the anonymous reviewers for their careful reviews, insightful comments and very useful suggestions. 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