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Calibration (statistics)

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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.
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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; 177:
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.
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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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about the value of a model's parameters, given some data set, or more generally to any type of fitting of a
737: 97: 87: 530: 93: 45: 282: 236: 105: 715: 539:," Classification Rules in Standardized Partition Spaces, Dissertation, Universität Dortmund, 2002 721:(eds.), Advances in Neural Information Processing Systems, volume 10, Cambridge, MIT Press, 1998. 352: – Subjective probabilities assigned in a way that historically represents their uncertainty 489:"Towards a Rigorous Calibration Assessment Framework: Advancements in Metrics, Methods, and Use" 326: 285:. The following multivariate calibration methods exist for transforming classifier scores into 188: 101: 28: 293:
Reduction to binary tasks and subsequent pairwise coupling, see Hastie and Tibshirani (1998)
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Bayesian Binning into Quantiles (BBQ) calibration, see Naeini, Cooper, Hauskrecht (2015)
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Ng, K. H., Pooi, A. H. (2008) "Calibration Intervals in Linear Regression Models",
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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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Multivariate calibration of classifier scores into the probability space
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Famiglini, Lorenzo; Campagner, Andrea; Cabitza, Federico (2023),
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employs the term "calibration" in this sense in his 2015 book
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Dawid, A. P (1982). "The Well-Calibrated Bayesian".
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Oxford: Oxford University Press. 146:Beta calibration, see Kull, Filho, 13: 124:Bayes approach, see Bennett (2002) 14: 759: 618:. Edge Foundation. 24 August 2015 375:Cook, Ian; Upton, Graham (2006). 350:Calibrated probability assessment 219: 210: 191:. For example, as expressed by 130:, see Zadrozny and Elkan (2002) 708: 694:Draper, N.L., Smith, H. (1998) 688: 668: 653: 633: 592: 582: 572: 562: 552: 542: 495:, IOS Press, pp. 645–652, 377:Oxford Dictionary of Statistics 31:problems. Calibration can mean 714:T. Hastie and R. Tibshirani, " 523: 480: 471: 461: 452: 443: 414:10.1080/01621459.1982.10477856 393: 368: 287:class membership probabilities 115:class membership probabilities 98:class membership probabilities 50:class membership probabilities 1: 361: 199:, in particular, as concerns 27:that denote special types of 88:Probabilistic classification 16:Ambiguous term in statistics 7: 337: 239:. The specific problem is: 10: 764: 748:Statistical classification 300: 158: 85: 74:puts it, "a forecaster is 46:statistical classification 743:Classification algorithms 283:sliced inverse regression 678:, 3 (4), 361–372. 117:in the two-class case: 663:, 37 (11), 1688–1696. 430:Gebel, Martin (2009). 321:. The observation is 189:accuracy and precision 241:unclear what it does. 187:. This differs from 37:a reverse process to 29:statistical inference 589:2015;2015:2901-2907. 356:Conformal prediction 246:improve this article 235:to meet Knowledge's 738:Regression analysis 639:Brown, P.J. (1994) 278:calibration problem 201:weather forecasting 138:logistic regression 128:Isotonic regression 535:2004-11-23 at the 501:10.3233/faia230327 319:radiometric dating 64:Bayesian inference 529:U. M. Garczarek " 386:978-0-19-954145-4 274: 273: 266: 237:quality standards 228:This article may 179:Philip E. Tetlock 82:In classification 68:statistical model 755: 722: 712: 706: 692: 686: 672: 666: 657: 651: 637: 631: 630: 625: 623: 608: 599: 596: 590: 586: 580: 576: 570: 566: 560: 556: 550: 546: 540: 527: 521: 520: 519: 517: 512: 484: 478: 475: 469: 465: 459: 456: 450: 447: 441: 440: 438: 427: 418: 417: 408:(379): 605–610. 397: 391: 390: 372: 311:dendrochronology 269: 262: 258: 255: 249: 223: 222: 215: 184:Superforecasting 763: 762: 758: 757: 756: 754: 753: 752: 728: 727: 726: 725: 713: 709: 693: 689: 673: 669: 658: 654: 638: 634: 621: 619: 610: 609: 602: 597: 593: 587: 583: 577: 573: 567: 563: 557: 553: 547: 543: 537:Wayback Machine 528: 524: 515: 513: 485: 481: 476: 472: 466: 462: 457: 453: 448: 444: 436: 428: 421: 398: 394: 387: 373: 369: 364: 340: 303: 270: 259: 253: 250: 243: 224: 220: 213: 193:Daniel Kahneman 163: 157: 92:Calibration in 90: 84: 76:well calibrated 17: 12: 11: 5: 761: 751: 750: 745: 740: 724: 723: 707: 687: 667: 652: 632: 600: 591: 581: 571: 561: 551: 541: 522: 479: 470: 460: 451: 442: 419: 392: 385: 366: 365: 363: 360: 359: 358: 353: 347: 339: 336: 302: 299: 298: 297: 294: 272: 271: 254:September 2023 227: 225: 218: 212: 209: 205:forecast skill 156: 153: 152: 151: 144: 141: 131: 125: 122: 94:classification 86:Main article: 83: 80: 56: 55: 54: 53: 44:procedures in 42: 15: 9: 6: 4: 3: 2: 760: 749: 746: 744: 741: 739: 736: 735: 733: 720: 716: 711: 705: 704:0-471-17082-8 701: 697: 691: 685: 681: 677: 676:Stata Journal 671: 665: 662: 656: 650: 649:0-19-852245-2 646: 642: 636: 629: 617: 613: 607: 605: 595: 585: 575: 565: 555: 545: 538: 534: 531: 526: 511: 506: 502: 498: 494: 490: 483: 474: 464: 455: 446: 435: 434: 426: 424: 415: 411: 407: 403: 396: 388: 382: 378: 371: 367: 357: 354: 351: 348: 345: 342: 341: 335: 333: 332:extrapolation 328: 324: 320: 316: 312: 308: 295: 292: 291: 290: 288: 284: 279: 268: 265: 257: 247: 242: 238: 234: 233: 226: 217: 216: 211:In regression 208: 206: 202: 198: 194: 190: 186: 185: 180: 176: 172: 168: 162: 149: 145: 142: 139: 135: 134:Platt scaling 132: 129: 126: 123: 120: 119: 118: 116: 110: 107: 103: 99: 95: 89: 79: 77: 73: 69: 65: 61: 51: 48:to determine 47: 43: 40: 36: 35: 34: 33: 32: 30: 26: 22: 710: 695: 690: 675: 670: 660: 655: 640: 635: 627: 620:. 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Index

statistics
statistical inference
regression
statistical classification
class membership probabilities
calibration
Bayesian inference
statistical model
Philip Dawid
Probabilistic classification
classification
class membership probabilities
two-class
multi-class
class membership probabilities
Isotonic regression
Platt scaling
logistic regression
Flach
Scoring rule
prediction
forecasting
Brier score
Philip E. Tetlock
Superforecasting
accuracy and precision
Daniel Kahneman
meteorology
weather forecasting
forecast skill

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