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Calibration (statistics) : Calibration β Check on the accuracy of measurement devices Calibrated probability assessment β Subjective probabilities assigned in a way that historically represents their uncertainty Conformal prediction == References == |
Soft independent modelling of class analogies : Soft independent modelling by class analogy (SIMCA) is a statistical method for supervised classification of data. The method requires a training data set consisting of samples (or objects) with a set of attributes and their class membership. The term soft refers to the f... |
Soft independent modelling of class analogies : In order to build the classification models, the samples belonging to each class need to be analysed using principal component analysis (PCA); only the significant components are retained. For a given class, the resulting model then describes either a line (for one Princi... |
Soft independent modelling of class analogies : SIMCA as a method of classification has gained widespread use especially in applied statistical fields such as chemometrics and spectroscopic data analysis. |
Soft independent modelling of class analogies : Wold, Svante, and Sjostrom, Michael, 1977, SIMCA: A method for analyzing chemical data in terms of similarity and analogy, in Kowalski, B.R., ed., Chemometrics Theory and Application, American Chemical Society Symposium Series 52, Wash., D.C., American Chemical Society, p... |
Statistical classification : When classification is performed by a computer, statistical methods are normally used to develop the algorithm. Often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. These properties may variously be cate... |
Statistical classification : Classification and clustering are examples of the more general problem of pattern recognition, which is the assignment of some sort of output value to a given input value. Other examples are regression, which assigns a real-valued output to each input; sequence labeling, which assigns a cla... |
Statistical classification : Early work on statistical classification was undertaken by Fisher, in the context of two-group problems, leading to Fisher's linear discriminant function as the rule for assigning a group to a new observation. This early work assumed that data-values within each of the two groups had a mult... |
Statistical classification : Unlike frequentist procedures, Bayesian classification procedures provide a natural way of taking into account any available information about the relative sizes of the different groups within the overall population. Bayesian procedures tend to be computationally expensive and, in the days ... |
Statistical classification : Classification can be thought of as two separate problems β binary classification and multiclass classification. In binary classification, a better understood task, only two classes are involved, whereas multiclass classification involves assigning an object to one of several classes. Since... |
Statistical classification : Most algorithms describe an individual instance whose category is to be predicted using a feature vector of individual, measurable properties of the instance. Each property is termed a feature, also known in statistics as an explanatory variable (or independent variable, although features m... |
Statistical classification : A large number of algorithms for classification can be phrased in terms of a linear function that assigns a score to each possible category k by combining the feature vector of an instance with a vector of weights, using a dot product. The predicted category is the one with the highest scor... |
Statistical classification : Since no single form of classification is appropriate for all data sets, a large toolkit of classification algorithms has been developed. The most commonly used include: Artificial neural networks β Computational model used in machine learning, based on connected, hierarchical functionsPage... |
Statistical classification : Classification has many applications. In some of these, it is employed as a data mining procedure, while in others more detailed statistical modeling is undertaken. Biological classification β The science of identifying, describing, defining and naming groups of biological organisms Biometr... |
Variable kernel density estimation : In statistics, adaptive or "variable-bandwidth" kernel density estimation is a form of kernel density estimation in which the size of the kernels used in the estimate are varied depending upon either the location of the samples or the location of the test point. It is a particularly... |
Variable kernel density estimation : Given a set of samples, _\rbrace , we wish to estimate the density, P ( x β ) ) , at a test point, x β : P ( x β ) β W n h D )\approx W = β i = 1 n w i ^w_ w i = K ( x β β x β i h ) =K\left(-_\right) where n is the number of samples, K is the "kernel", h is its width and D is th... |
Variable kernel density estimation : A common method of varying the kernel width is to make it inversely proportional to the density at the test point: h = k [ n P ( x β ) ] 1 / D )\right]^ where k is a constant. If we back-substitute the estimated PDF, and assuming a Gaussian kernel function, we can show that W is a c... |
Variable kernel density estimation : The method is particularly effective when applied to statistical classification. There are two ways we can proceed: the first is to compute the PDFs of each class separately, using different bandwidth parameters, and then compare them as in Taylor. Alternatively, we can divide up th... |
Variable kernel density estimation : akde1d.m - Matlab m-file for one-dimensional adaptive kernel density estimation. libAGF - A C++ library for multivariate adaptive kernel density estimation. akde.m - Matlab function for multivariate (high-dimensional) variable kernel density estimation. == References == |
(1+Ξ΅)-approximate nearest neighbor search : (1+Ξ΅)-approximate nearest neighbor search is a variant of the nearest neighbor search problem. A solution to the (1+Ξ΅)-approximate nearest neighbor search is a point or multiple points within distance (1+Ξ΅) R from a query point, where R is the distance between the query point... |
Alternating decision tree : An alternating decision tree (ADTree) is a machine learning method for classification. It generalizes decision trees and has connections to boosting. An ADTree consists of an alternation of decision nodes, which specify a predicate condition, and prediction nodes, which contain a single numb... |
Alternating decision tree : ADTrees were introduced by Yoav Freund and Llew Mason. However, the algorithm as presented had several typographical errors. Clarifications and optimizations were later presented by Bernhard Pfahringer, Geoffrey Holmes and Richard Kirkby. Implementations are available in Weka and JBoost. |
Alternating decision tree : Original boosting algorithms typically used either decision stumps or decision trees as weak hypotheses. As an example, boosting decision stumps creates a set of T weighted decision stumps (where T is the number of boosting iterations), which then vote on the final classification according... |
Alternating decision tree : An alternating decision tree consists of decision nodes and prediction nodes. Decision nodes specify a predicate condition. Prediction nodes contain a single number. ADTrees always have prediction nodes as both root and leaves. An instance is classified by an ADTree by following all paths fo... |
Alternating decision tree : The inputs to the alternating decision tree algorithm are: A set of inputs ( x 1 , y 1 ) , β¦ , ( x m , y m ) ,y_),\ldots ,(x_,y_) where x i is a vector of attributes and y i is either -1 or 1. Inputs are also called instances. A set of weights w i corresponding to each instance. The funda... |
Alternating decision tree : Figure 6 in the original paper demonstrates that ADTrees are typically as robust as boosted decision trees and boosted decision stumps. Typically, equivalent accuracy can be achieved with a much simpler tree structure than recursive partitioning algorithms. |
Alternating decision tree : An introduction to Boosting and ADTrees (Has many graphical examples of alternating decision trees in practice). JBoost software implementing ADTrees. |
Analogical modeling : Analogical modeling (AM) is a formal theory of exemplar based analogical reasoning, proposed by Royal Skousen, professor of Linguistics and English language at Brigham Young University in Provo, Utah. It is applicable to language modeling and other categorization tasks. Analogical modeling is rela... |
Analogical modeling : Analogy has been considered useful in describing language at least since the time of Saussure. Noam Chomsky and others have more recently criticized analogy as too vague to really be useful (BaΕko 1991), an appeal to a deus ex machina. Skousen's proposal appears to address that criticism by propos... |
Analogical modeling : Analogical modeling has been employed in experiments ranging from phonology and morphology (linguistics) to orthography and syntax. |
Analogical modeling : Though analogical modeling aims to create a model free from rules seen as contrived by linguists, in its current form it still requires researchers to select which variables to take into consideration. This is necessary because of the so-called "exponential explosion" of processing power requireme... |
Analogical modeling : Computational Linguistics Connectionism Instance-based learning k-nearest neighbor algorithm |
Analogical modeling : Royal Skousen (1989). Analogical Modeling of Language (hardcover). Dordrecht: Kluwer Academic Publishers. xii+212pp. ISBN 0-7923-0517-5. Miroslaw BaΕko (June 1991). "Review: Analogical Modeling of Language" (PDF). Computational Linguistics. 17 (2): 246β248. Archived from the original (PDF) on 2003... |
Analogical modeling : Analogical Modeling Research Group Homepage LINGUIST List Announcement of Analogical Modeling, Skousen et al. (2002) |
Averaged one-dependence estimators : Averaged one-dependence estimators (AODE) is a probabilistic classification learning technique. It was developed to address the attribute-independence problem of the popular naive Bayes classifier. It frequently develops substantially more accurate classifiers than naive Bayes at th... |
Averaged one-dependence estimators : AODE seeks to estimate the probability of each class y given a specified set of features x1, ... xn, P(y | x1, ... xn). To do so it uses the formula P ^ ( y β£ x 1 , β¦ x n ) = β i : 1 β€ i β€ n β§ F ( x i ) β₯ m P ^ ( y , x i ) β j = 1 n P ^ ( x j β£ y , x i ) β y β² β Y β i : 1 β€ i β€ n β§ ... |
Averaged one-dependence estimators : We seek to estimate P(y | x1, ... xn). By the definition of conditional probability P ( y β£ x 1 , β¦ x n ) = P ( y , x 1 , β¦ x n ) P ( x 1 , β¦ x n ) . ,\ldots x_)=,\ldots x_),\ldots x_). For any 1 β€ i β€ n , P ( y , x 1 , β¦ x n ) = P ( y , x i ) P ( x 1 , β¦ x n β£ y , x i ) . ,\ldots ... |
Averaged one-dependence estimators : Like naive Bayes, AODE does not perform model selection and does not use tuneable parameters. As a result, it has low variance. It supports incremental learning whereby the classifier can be updated efficiently with information from new examples as they become available. It predicts... |
Averaged one-dependence estimators : The free Weka machine learning suite includes an implementation of AODE. |
Averaged one-dependence estimators : Cluster-weighted modeling == References == |
Automated Pain Recognition : Automated Pain Recognition (APR) is a method for objectively measuring pain and at the same time represents an interdisciplinary research area that comprises elements of medicine, psychology, psychobiology, and computer science. The focus is on computer-aided objective recognition of pain, ... |
Automated Pain Recognition : Pain diagnosis under conditions where verbal reporting is restricted - such as in verbally and/or cognitively impaired people or in patients who are sedated or mechanically ventilated - is based on behavioral observations by trained professionals. However, all known observation procedures (... |
Automated Pain Recognition : For automated pain recognition, pain-relevant parameters are usually recorded using non-invasive sensor technology, which captures data on the (physical) responses of the person in pain. This can be achieved with camera technology that captures facial expressions, gestures, or posture, whil... |
Automated Pain Recognition : Although the phenomenon of pain comprises different components (sensory discriminative, affective (emotional), cognitive, vegetative, and (psycho-)motor), automated pain recognition currently relies on the measurable parameters of pain responses. These can be divided roughly into the two ma... |
Automated Pain Recognition : After the recording, pre-processing (e.g., filtering), and extraction of relevant features, an optional information fusion can be performed. During this process, modalities from different signal sources are merged to generate new or more precise knowledge. The pain is classified using machi... |
Automated Pain Recognition : In order to classify pain in a valid manner, it is necessary to create representative, reliable, and valid pain databases that are available to the machine learner for training. An ideal database would be sufficiently large and would consist of natural (not experimental), high-quality pain ... |
Automated Pain Recognition : Automated Pain Research Group at the University of Ulm, Germany |
C4.5 algorithm : C4.5 is an algorithm used to generate a decision tree developed by Ross Quinlan. C4.5 is an extension of Quinlan's earlier ID3 algorithm. The decision trees generated by C4.5 can be used for classification, and for this reason, C4.5 is often referred to as a statistical classifier. In 2011, authors of ... |
C4.5 algorithm : C4.5 builds decision trees from a set of training data in the same way as ID3, using the concept of information entropy. The training data is a set S = s 1 , s 2 , . . . ,s_,... of already classified samples. Each sample s i consists of a p-dimensional vector ( x 1 , i , x 2 , i , . . . , x p , i ) ,x... |
C4.5 algorithm : J48 is an open source Java implementation of the C4.5 algorithm in the Weka data mining tool. |
C4.5 algorithm : C4.5 made a number of improvements to ID3. Some of these are: Handling both continuous and discrete attributes - In order to handle continuous attributes, C4.5 creates a threshold and then splits the list into those whose attribute value is above the threshold and those that are less than or equal to i... |
C4.5 algorithm : Quinlan went on to create C5.0 and See5 (C5.0 for Unix/Linux, See5 for Windows) which he markets commercially. C5.0 offers a number of improvements on C4.5. Some of these are: Speed - C5.0 is significantly faster than C4.5 (several orders of magnitude) Memory usage - C5.0 is more memory efficient than ... |
C4.5 algorithm : ID3 algorithm Modifying C4.5 to generate temporal and causal rules |
C4.5 algorithm : Original implementation on Ross Quinlan's homepage: http://www.rulequest.com/Personal/ See5 and C5.0 |
Chi-square automatic interaction detection : Chi-square automatic interaction detection (CHAID) is a decision tree technique based on adjusted significance testing (Bonferroni correction, Holm-Bonferroni testing). |
Chi-square automatic interaction detection : CHAID is based on a formal extension of AID (Automatic Interaction Detection) and THAID (THeta Automatic Interaction Detection) procedures of the 1960s and 1970s, which in turn were extensions of earlier research, including that performed by Belson in the UK in the 1950s. In... |
Chi-square automatic interaction detection : CHAID can be used for prediction (in a similar fashion to regression analysis, this version of CHAID being originally known as XAID) as well as classification, and for detection of interaction between variables. In practice, CHAID is often used in the context of direct marke... |
Chi-square automatic interaction detection : Bonferroni correction Chi-squared distribution Decision tree learning Latent class model Market segment Multiple comparisons Structural equation modeling |
Chi-square automatic interaction detection : Press, Laurence I.; Rogers, Miles S.; & Shure, Gerald H.; An interactive technique for the analysis of multivariate data, Behavioral Science, Vol. 14 (1969), pp. 364β370 Hawkins, Douglas M.; and Kass, Gordon V.; Automatic Interaction Detection, in Hawkins, Douglas M. (ed), T... |
Chi-square automatic interaction detection : Luchman, J.N.; CHAID: Stata module to conduct chi-square automated interaction detection, Available for free download, or type within Stata: ssc install chaid. Luchman, J.N.; CHAIDFOREST: Stata module to conduct random forest ensemble classification based on chi-square autom... |
Classifier chains : Classifier chains is a machine learning method for problem transformation in multi-label classification. It combines the computational efficiency of the binary relevance method while still being able to take the label dependencies into account for classification. |
Classifier chains : Several problem transformation methods exist. One of them is the Binary Relevance method (BR). Given a set of labels L \, and a data set with instances of the form ( x , Y ) \, where x \, is a feature vector and Y β L is a set of labels assigned to the instance. BR transforms the data set into | L ... |
Classifier chains : For a given set of labels L \, the Classifier Chain model (CC) learns | L | classifiers as in the Binary Relevance method. All classifiers are linked in a chain through feature space. Given a data set where the i -th instance has the form ( x i , Y i ) ,Y_)\, where Y i \, is a subset of labels, x ... |
Classifier chains : There is also regressor chains, which themselves can resemble vector autoregression models if the order of the chain makes sure temporal order is respected. |
Classifier chains : Better Classifier Chains for Multi-label Classification Presentation on Classifier Chains by Jesse Read and Fernando PΓ©rez Cruz |
Co-training : Co-training is a machine learning algorithm used when there are only small amounts of labeled data and large amounts of unlabeled data. One of its uses is in text mining for search engines. It was introduced by Avrim Blum and Tom Mitchell in 1998. |
Co-training : Co-training is a semi-supervised learning technique that requires two views of the data. It assumes that each example is described using two different sets of features that provide complementary information about the instance. Ideally, the two views are conditionally independent (i.e., the two feature set... |
Co-training : Co-training has been used to classify web pages using the text on the page as one view and the anchor text of hyperlinks on other pages that point to the page as the other view. Simply put, the text in a hyperlink on one page can give information about the page it links to. Co-training can work on "unlabe... |
Co-training : Notes Chakrabarti, Soumen (2002). Mining the Web: Discovering Knowledge from Hypertext Data. Morgan-Kaufmann Publishers. p. 352. ISBN 978-1-55860-754-5. Nigam, Kamal; Rayid Ghani (2000). "Analyzing the Effectiveness and Applicability of Co-training". Proceedings of the Ninth International Conference on In... |
Co-training : Lecture by Tom Mitchell introducing co-training and other semi-supervised machine learning for use on unlabeled data Lecture by Avrim Blum on semi-supervised learning, including co-training Co-Training group at Pittsburgh Science of Learning Center |
CoBoosting : CoBoost is a semi-supervised training algorithm proposed by Collins and Singer in 1999. The original application for the algorithm was the task of named-entity recognition using very weak learners, but it can be used for performing semi-supervised learning in cases where data features may be redundant. It ... |
CoBoosting : CoBoosting was an attempt by Collins and Singer to improve on previous attempts to leverage redundancy in features for training classifiers in a semi-supervised fashion. CoTraining, a seminal work by Blum and Mitchell, was shown to be a powerful framework for learning classifiers given a small number of se... |
CoBoosting : Input: i = 1 n ,x_)\_^ , i = 1 m \_^ Initialize: β i , j : g j 0 ( x i ) = 0 ^()=0 . For t = 1 , . . . , T and for j = 1 , 2 : Set pseudo-labels: y i ^ = =\left\y_,1\leq i\leq m\\sign(g_^()),m<i\leq n\end\right. Set virtual distribution: D t j ( i ) = 1 Z t j e β y i ^ g j t β 1 ( x j , i ) ^(i)=^e^g_^... |
CoBoosting : CoBoosting builds on the AdaBoost algorithm, which gives CoBoosting its generalization ability since AdaBoost can be used in conjunction with many other learning algorithms. This build up assumes a two class classification task, although it can be adapted to multiple class classification. In the AdaBoost f... |
CoBoosting : CoBoosting extends this framework in the case where one has a labeled training set (examples from 1... m ) and an unlabeled training set (from m 1 . . . n ...n ), as well as satisfy the conditions of redundancy in features in the form of x i = ( x 1 , i , x 2 , i ) =(x_,x_) . The algorithm trains two clas... |
CoBoosting : === Footnotes === |
Decision boundary : In a statistical-classification problem with two classes, a decision boundary or decision surface is a hypersurface that partitions the underlying vector space into two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one clas... |
Decision boundary : In the case of backpropagation based artificial neural networks or perceptrons, the type of decision boundary that the network can learn is determined by the number of hidden layers the network has. If it has no hidden layers, then it can only learn linear problems. If it has one hidden layer, then ... |
Decision boundary : Discriminant function Hyperplane separation theorem |
Decision boundary : Duda, Richard O.; Hart, Peter E.; Stork, David G. (2001). Pattern Classification (2nd ed.). New York: Wiley. pp. 215β281. ISBN 0-471-05669-3. |
Decision tree learning : Decision tree learning is a supervised learning approach used in statistics, data mining and machine learning. In this formalism, a classification or regression decision tree is used as a predictive model to draw conclusions about a set of observations. Tree models where the target variable can... |
Decision tree learning : Decision tree learning is a method commonly used in data mining. The goal is to create a model that predicts the value of a target variable based on several input variables. A decision tree is a simple representation for classifying examples. For this section, assume that all of the input featu... |
Decision tree learning : Decision trees used in data mining are of two main types: Classification tree analysis is when the predicted outcome is the class (discrete) to which the data belongs. Regression tree analysis is when the predicted outcome can be considered a real number (e.g. the price of a house, or a patient... |
Decision tree learning : Algorithms for constructing decision trees usually work top-down, by choosing a variable at each step that best splits the set of items. Different algorithms use different metrics for measuring "best". These generally measure the homogeneity of the target variable within the subsets. Some examp... |
Decision tree learning : James, Gareth; Witten, Daniela; Hastie, Trevor; Tibshirani, Robert (2017). "Tree-Based Methods" (PDF). An Introduction to Statistical Learning: with Applications in R. New York: Springer. pp. 303β336. ISBN 978-1-4614-7137-0. |
Decision tree learning : Evolutionary Learning of Decision Trees in C++ A very detailed explanation of information gain as splitting criterion |
Elastic matching : Elastic matching is one of the pattern recognition techniques in computer science. Elastic matching (EM) is also known as deformable template, flexible matching, or nonlinear template matching. Elastic matching can be defined as an optimization problem of two-dimensional warping specifying correspond... |
Elastic matching : Uchida, Seiichi (August 2005). "A Survey of Elastic Matching Techniques for Handwritten Character Recognition" (PDF). IEICE Transactions on Information and Systems. E88-D (8): 1781β1790. Bibcode:2005IEITI..88.1781U. doi:10.1093/ietisy/e88-d.8.1781. |
Elastic matching : Dynamic time warping Graphical time warping |
Generalization error : For supervised learning applications in machine learning and statistical learning theory, generalization error (also known as the out-of-sample error or the risk) is a measure of how accurately an algorithm is able to predict outcomes for previously unseen data. As learning algorithms are evaluat... |
Generalization error : In a learning problem, the goal is to develop a function f n ( x β ) () that predicts output values y for each input datum x β . The subscript n indicates that the function f n is developed based on a data set of n data points. The generalization error or expected loss or risk I [ f ] of a ... |
Generalization error : The concepts of generalization error and overfitting are closely related. Overfitting occurs when the learned function f S becomes sensitive to the noise in the sample. As a result, the function will perform well on the training set but not perform well on other data from the joint probability d... |
Generalization error : Olivier, Bousquet; Luxburg, Ulrike; RΓ€tsch, Gunnar, eds. (2004). Advanced Lectures on Machine Learning. Lecture Notes in Computer Science. Vol. 3176. pp. 169β207. doi:10.1007/b100712. ISBN 978-3-540-23122-6. S2CID 431437. Retrieved 10 December 2022. Bousquet, Olivier; Elisseeff, AndrΒ΄e (1 March 2... |
Gesture Description Language : Gesture Description Language (GDL or GDL Technology) is a method of describing and automatic (computer) syntactic classification of gestures and movements created by doctor Tomasz Hachaj (PhD) and professor Marek R. Ogiela(PhD, DSc). GDL uses context-free formal grammar named GDLs (Gestur... |
ID3 algorithm : In decision tree learning, ID3 (Iterative Dichotomiser 3) is an algorithm invented by Ross Quinlan used to generate a decision tree from a dataset. ID3 is the precursor to the C4.5 algorithm, and is typically used in the machine learning and natural language processing domains. |
ID3 algorithm : The ID3 algorithm begins with the original set S as the root node. On each iteration of the algorithm, it iterates through every unused attribute of the set S and calculates the entropy H ( S ) or the information gain I G ( S ) of that attribute. It then selects the attribute which has the smallest... |
ID3 algorithm : Classification and regression tree (CART) C4.5 algorithm Decision tree learning Decision tree model |
ID3 algorithm : Mitchell, Tom Michael (1997). Machine Learning. New York, NY: McGraw-Hill. pp. 55β58. ISBN 0070428077. OCLC 36417892. Grzymala-Busse, Jerzy W. (February 1993). "Selected Algorithms of Machine Learning from Examples" (PDF). Fundamenta Informaticae. 18 (2): 193β207 β via ResearchGate. |
ID3 algorithm : Seminars β http://www2.cs.uregina.ca/ Description and examples β http://www.cise.ufl.edu/ Description and examples β http://www.cis.temple.edu/ Decision Trees and Political Party Classification |
Information gain (decision tree) : In information theory and machine learning, information gain is a synonym for KullbackβLeibler divergence; the amount of information gained about a random variable or signal from observing another random variable. However, in the context of decision trees, the term is sometimes used s... |
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