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tendencies. Originally formulated for binary settings, the ECI has been adapted for multiclass settings, offering both local and global insights into model calibration. This framework aims to overcome some of the theoretical and interpretative limitations of existing calibration metrics. Through a series of experiments, Famiglini et al. demonstrate the framework's effectiveness in delivering a more accurate understanding of model calibration levels and discuss strategies for mitigating biases in calibration assessment. An online tool has been proposed to compute both ECE and ECI. The following univariate calibration methods exist for transforming classifier scores into
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metrics exist that are aimed to measure the extent to which a classifier produces well-calibrated probabilities. Foundational work includes the
Expected Calibration Error (ECE). Into the 2020s, variants include the Adaptive Calibration Error (ACE) and the Test-based Calibration Error (TCE), which address limitations of the ECE metric that may arise when classifier scores concentrate on narrow subset of the range.
221:
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D. D. Lewis and W. A. Gale, A Sequential
Algorithm for Training Text classifiers. In: W. B. Croft and C. J. van Rijsbergen (eds.), Proceedings of the 17th Annual International ACM SIGIR Conference on Research and Development in Information Retrieval (SIGIR '94), 3–12. New York, Springer-Verlag,
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classification tasks is given by Gebel (2009). A classifier might separate the classes well, but be poorly calibrated, meaning that the estimated class probabilities are far from the true class probabilities. In this case, a calibration step may help improve the estimated probabilities. A variety of
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A 2020s advancement in calibration assessment is the introduction of the
Estimated Calibration Index (ECI). The ECI extends the concepts of the Expected Calibration Error (ECE) to provide a more nuanced measure of a model's calibration, particularly addressing overconfidence and underconfidence
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in regression is the use of known data on the observed relationship between a dependent variable and an independent variable to make estimates of other values of the independent variable from new observations of the dependent variable. This can be known as "inverse regression"; there is also
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is whether the model used for relating known ages with observations should aim to minimise the error in the observation, or minimise the error in the date. The two approaches will produce different results, and the difference will increase if the model is then used for
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J. C. Platt, Probabilistic outputs for support vector machines and comparisons to regularized likelihood methods. In: A. J. Smola, P. Bartlett, B. Schölkopf and D. Schuurmans (eds.), Advances in Large Margin
Classiers, 61–74. Cambridge, MIT Press,
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B. Zadrozny and C. Elkan, Transforming classifier scores into accurate multiclass probability estimates. In: Proceedings of the Eighth
International Conference on Knowledge Discovery and Data Mining, 694–699, Edmonton, ACM Press,
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P. N. Bennett, Using asymmetric distributions to improve text classifier probability estimates: A comparison of new and standard parametric methods, Technical Report CMU-CS-02-126, Carnegie Mellon, School of
Computer Science,
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Famiglini, Lorenzo, Andrea
Campagner, and Federico Cabitza. "Towards a Rigorous Calibration Assessment Framework: Advancements in Metrics, Methods, and Use." ECAI 2023. IOS Press, 2023. 645-652. Doi 10.3233/FAIA230327
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Naeini MP, Cooper GF, Hauskrecht M. Obtaining Well
Calibrated Probabilities Using Bayesian Binning. Proceedings of the . AAAI Conference on Artificial Intelligence AAAI Conference on Artificial Intelligence.
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T. Matsubara, N. Tax, R. Mudd, & I. Guy. TCE: A Test-Based
Approach to Measuring Calibration Error. In: Proceedings of the Thirty-Ninth Conference on Uncertainty in Artificial Intelligence (UAI), PMLR,
41:, where instead of a future dependent variable being predicted from known explanatory variables, a known observation of the dependent variables is used to predict a corresponding explanatory variable;
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is sometimes used to assess prediction accuracy of a set of predictions, specifically that the magnitude of the assigned probabilities track the relative frequency of the observed outcomes.
195:, "if you give all events that happen a probability of .6 and all the events that don't happen a probability of .4, your calibration is perfect but your discrimination is miserable". In
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M.P. Naeini, G. Cooper, and M. Hauskrecht, Obtaining well calibrated probabilities using bayesian binning. In: Proceedings of the AAAI Conference on
Artificial Intelligence, 2015.
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Hardin, J. W., Schmiediche, H., Carroll, R. J. (2003) "The regression-calibration method for fitting generalized linear models with additive measurement error",
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Meelis Kull, Telmo Silva Filho, Peter Flach; Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:623-631, 2017.
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if, for example, of those events to which he assigns a probability 30 percent, the long-run proportion that actually occurs turns out to be 30 percent."
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by the age of the object being dated, rather than the reverse, and the aim is to use the method for estimating dates based on new observations. The
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J. Nixon, M.W. Dusenberry, L. Zhang, G. Jerfel, & D. Tran. Measuring Calibration in Deep Learning. In: CVPR workshops (Vol. 2, No. 7), 2019.
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Calibration is when I say there's a 70 percent likelihood of something happening, things happen 70 percent of time.
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which assess the uncertainty of a given new observation belonging to each of the already established classes.
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489:"Towards a Rigorous Calibration Assessment Framework: Advancements in Metrics, Methods, and Use"
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285:. The following multivariate calibration methods exist for transforming classifier scores into
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Bayesian Binning into Quantiles (BBQ) calibration, see Naeini, Cooper, Hauskrecht (2015)
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In addition, calibration is used in statistics with the usual general meaning of
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One example is that of dating objects, using observable evidence such as
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employs the term "calibration" in this sense in his 2015 book
62:. For example, model calibration can be also used to refer to
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Dawid, A. P (1982). "The Well-Calibrated Bayesian".
346: – Check on the accuracy of measurement devices
661:Communications in Statistics - Theory and Methods
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140:), see Lewis and Gale (1994) and Platt (1999)
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264:Learn how and when to remove this message
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296:Dirichlet calibration, see Gebel (2009)
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146:Beta calibration, see Kull, Filho,
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350:Calibrated probability assessment
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278:calibration problem
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