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probabilistic classification wikipedia jump to content main menu main menu move to sidebar hide navigation main page contents current events random article about wikipedia contact us contribute help learn to edit community portal recent changes upload file special pages search search appearance donate create account log in personal tools donate create account log in contents move to sidebar hide top 1 types of classification 2 generative and conditional training 3 probability calibration 4 evaluating probabilistic classification 5 software implementations 6 references toggle the table of contents probabilistic classification 5 languages català deutsch italiano русский українська edit links article talk english read edit view history tools tools move to sidebar hide actions read edit view history general what links here related changes upload file permanent link page information cite this page get shortened url switch to legacy parser print export download as pdf printable version in other projects wikidata item appearance move to sidebar hide from wikipedia the free encyclopedia redirected from group membership probabilities machine learning problem part of a series on machine learning and data mining paradigms supervised learning unsupervised learning semi supervised learning self supervised learning reinforcement learning transfer learning meta learning few shot learning zero shot learning online learning batch learning curriculum learning rule based learning neuro symbolic ai neuromorphic engineering quantum machine learning problems classification generative modeling regression clustering dimensionality reduction density estimation anomaly detection data cleaning automl association rules semantic analysis structured prediction feature engineering feature learning learning to rank grammar induction ontology learning multimodal learning supervised learning classification regression apprenticeship learning decision trees ensembles bagging boosting random forest k nn linear regression naive bayes artificial neural networks logistic regression perceptron relevance vector machine rvm support vector machine svm clustering birch cure hierarchical k means fuzzy expectation maximization em dbscan optics mean shift dimensionality reduction factor analysis exploratory cca ica lda nmf pca pgd t sne sdl structured prediction graphical models bayes net conditional random field hidden markov anomaly detection ransac k nn local outlier factor isolation forest neural networks autoencoder deep learning feedforward neural network recurrent neural network lstm gru esn reservoir computing boltzmann machine restricted gan diffusion model som convolutional neural network u net lenet alexnet deepdream neural field neural radiance field physics informed neural networks transformer vision mamba spiking neural network memtransistor electrochemical ram ecram reinforcement learning q learning policy gradient sarsa temporal difference td multi agent self play learning with humans active learning crowdsourcing human in the loop mechanistic interpretability rlhf model diagnostics coefficient of determination confusion matrix learning curve roc curve mathematical foundations kernel machines bias variance tradeoff computational learning theory empirical risk minimization occam learning pac learning statistical learning vc theory topological deep learning journals and conferences aaai cvpr eccv ecml pkdd emnlp iccv neurips icml iclr ijcai ml jmlr related articles glossary of artificial intelligence list of datasets for machine learning research list of datasets in computer vision and image processing outline of machine learning v t e in machine learning a probabilistic classifier is a classifier that is able to predict given an observation of an input a probability distribution over a set of classes rather than only outputting the most likely class that the observation should belong to probabilistic classifiers provide classification that can be useful in its own right 1 or when combining classifiers into ensembles types of classification edit formally an ordinary classifier is some rule or function that assigns to a sample x a class label ŷ y f x displaystyle hat y f x the samples come from some set x e g the set of all documents or the set of all images while the class labels form a finite set y defined prior to training probabilistic classifiers generalize this notion of classifiers instead of functions they are conditional distributions pr y x displaystyle pr y vert x meaning that for a given x x displaystyle x in x they assign probabilities to all y y displaystyle y in y and these probabilities sum to one hard classification can then be done using the optimal decision rule 2 39 40 y arg max y pr y y x displaystyle hat y operatorname arg max _ y pr y y vert x or in english the predicted class is that which has the highest probability binary probabilistic classifiers are also called binary regression models in statistics in econometrics probabilistic classification in general is called discrete choice some classification models such as naive bayes logistic regression and multilayer perceptrons when trained under an appropriate loss function are naturally probabilistic other models such as support vector machines are not but methods exist to turn them into probabilistic classifiers generative and conditional training edit some models such as logistic regression are conditionally trained they optimize the conditional probability pr y x displaystyle pr y vert x directly on a training set see empirical risk minimization other classifiers such as naive bayes are trained generatively at training time the class conditional distribution pr x y displaystyle pr x vert y and the class prior pr y displaystyle pr y are found and the conditional distribution pr y x displaystyle pr y vert x is derived using bayes rule 2 43 probability calibration edit main article calibration statistics not all classification models are naturally probabilistic and some that are notably naive bayes classifiers decision trees and boosting methods produce distorted class probability distributions 3 in the case of decision trees where pr y x is the proportion of training samples with label y in the leaf where x ends up these distortions come about because learning algorithms such as c4 5 or cart explicitly aim to produce homogeneous leaves giving probabilities close to zero or one and thus high bias while using few samples to estimate the relevant proportion high variance 4 an example calibration plot calibration can be assessed using a calibration plot also called a reliability diagram 3 5 a calibration plot shows the proportion of items in each class for bands of predicted probability or score such as a distorted probability distribution or the signed distance to the hyperplane in a support vector machine deviations from the identity function indicate a poorly calibrated classifier for which the predicted probabilities or scores can not be used as probabilities in this case one can use a method to turn these scores into properly calibrated class membership probabilities for the binary case a common approach is to apply platt scaling which learns a logistic regression model on the scores 6 an alternative method using isotonic regression 7 is generally superior to platt s method when sufficient training data is available 3 in the multiclass case one can use a reduction to binary tasks followed by univariate calibration with an algorithm as described above and further application of the pairwise coupling algorithm by hastie and tibshirani 8 evaluating probabilistic classification edit models are assessed via accuracy calibration sharpness minimal uncertainty and dispersion similar uncertainties everywhere a method used to assign scores to pairs of predicted probabilities and actual discrete outcomes so that different predictive methods can be compared is called a scoring rule scoring rules are used to compare the predicted probability to observed outcomes these include for example log loss brier score continuous ranked probability score and others specific aspects like accuracy calibration sharpness or dispersion may vary from one probabilistic classifier to another one and may be specifically investigated calibration errors metrics aim to quantify the extent to which a probabilistic classifier s outputs are well calibrated as philip dawid put it a forecaster is well calibrated 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 9 foundational work in the domain of measuring calibration error is the expected calibration error ece metric 10 more recent works propose variants to ece that address limitations of the ece metric that may arise when classifier scores concentrate on narrow subset of the 0 1 including the adaptive calibration error ace 11 and test based calibration error tce 12 software implementations edit morpe 13 is a trainable probabilistic classifier that uses isotonic regression for probability calibration it solves the multiclass case by reduction to binary tasks it is a type of kernel machine that uses an inhomogeneous polynomial kernel references edit hastie trevor tibshirani robert friedman jerome 2009 the elements of statistical learning p 348 archived from the original on 2015 01 26 i n data mining applications the interest is often more in the class probabilities p ℓ x ℓ 1 k displaystyle p_ ell x ell 1 dots k themselves rather than in performing a class assignment 1 2 bishop christopher m 2006 pattern recognition and machine learning pdf springer isbn 978 0387 31073 2 1 2 3 niculescu mizil alexandru caruana rich 2005 predicting good probabilities with supervised learning pdf icml doi 10 1145 1102351 1102430 archived from the original pdf on 2014 03 11 zadrozny bianca elkan charles 2001 obtaining calibrated probability estimates from decision trees and naive bayesian classifiers pdf icml pp 609 616 probability calibration jmetzen github io retrieved 2019 06 18 platt john 1999 probabilistic outputs for support vector machines and comparisons to regularized likelihood methods advances in large margin classifiers 10 3 61 74 zadrozny bianca elkan charles 2002 transforming classifier scores into accurate multiclass probability estimates pdf proceedings of the eighth acm sigkdd international conference on knowledge discovery and data mining kdd 02 pp 694 699 doi 10 1145 775047 775151 isbn 978 1 58113 567 1 s2cid 3349576 citeseerx 10 1 1 13 7457 cite book cs1 maint miscellaneous url link hastie trevor tibshirani robert 1998 classification by pairwise coupling the annals of statistics 26 2 451 471 doi 10 1214 aos 1028144844 zbl 0932 62071 citeseerx 10 1 1 46 6032 cite journal cs1 maint miscellaneous url link dawid a p 1982 the well calibrated bayesian journal of the american statistical association 77 379 605 610 doi 10 1080 01621459 1982 10477856 naeini m p cooper g hauskrecht m 2015 obtaining well calibrated probabilities using bayesian binning pdf proceedings of the aaai conference on artificial intelligence nixon j dusenberry m w zhang l jerfel g tran d 2019 measuring calibration in deep learning pdf cvpr workshops matsubara t tax n mudd r guy i 2023 tce a test based approach to measuring calibration error proceedings of the thirty ninth conference on uncertainty in artificial intelligence uai arxiv 2306 14343 morpe github retrieved 17 february 2023 retrieved from https en wikipedia org w index php title probabilistic_classification oldid 1379748842 categories probabilistic models statistical classification hidden categories articles with short description short description matches wikidata cs1 maint miscellaneous url this page was last edited on 11 october 2026 at 18 51 utc page was rendered with parsoid text is available under the creative commons attribution sharealike 4 0 license additional terms 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