|
Platt Scaling
In machine learning, Platt scaling or Platt calibration is a way of transforming the outputs of a classification model into a probability distribution over classes. The method was invented by John Platt in the context of support vector machines, replacing an earlier method by Vapnik, but can be applied to other classification models. Platt scaling works by fitting a logistic regression model to a classifier's scores. Description Consider the problem of binary classification: for inputs , we want to determine whether they belong to one of two classes, arbitrarily labeled and . We assume that the classification problem will be solved by a real-valued function , by predicting a class label . For many problems, it is convenient to get a probability P(y=1, x), i.e. a classification that not only gives an answer, but also a degree of certainty about the answer. Some classification models do not provide such a probability, or give poor probability estimates. Platt scaling is an algo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning
Machine learning (ML) is a field of inquiry devoted to understanding and building methods that 'learn', that is, methods that leverage data to improve performance on some set of tasks. It is seen as a part of artificial intelligence. Machine learning algorithms build a model based on sample data, known as training data, in order to make predictions or decisions without being explicitly programmed to do so. Machine learning algorithms are used in a wide variety of applications, such as in medicine, email filtering, speech recognition, agriculture, and computer vision, where it is difficult or unfeasible to develop conventional algorithms to perform the needed tasks.Hu, J.; Niu, H.; Carrasco, J.; Lennox, B.; Arvin, F.,Voronoi-Based Multi-Robot Autonomous Exploration in Unknown Environments via Deep Reinforcement Learning IEEE Transactions on Vehicular Technology, 2020. A subset of machine learning is closely related to computational statistics, which focuses on making predicti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Bayes' Rule
In probability theory and statistics, Bayes' theorem (alternatively Bayes' law or Bayes' rule), named after Thomas Bayes, describes the probability of an event, based on prior knowledge of conditions that might be related to the event. For example, if the risk of developing health problems is known to increase with age, Bayes' theorem allows the risk to an individual of a known age to be assessed more accurately (by conditioning it on their age) than simply assuming that the individual is typical of the population as a whole. One of the many applications of Bayes' theorem is Bayesian inference, a particular approach to statistical inference. When applied, the probabilities involved in the theorem may have different probability interpretations. With Bayesian probability interpretation, the theorem expresses how a degree of belief, expressed as a probability, should rationally change to account for the availability of related evidence. Bayesian inference is fundamental to Bayesi ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relevance Vector Machine
In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. The RVM has an identical functional form to the support vector machine, but provides probabilistic classification. It is actually equivalent to a Gaussian process model with covariance function: :k(\mathbf,\mathbf) = \sum_^N \frac \varphi(\mathbf,\mathbf_j)\varphi(\mathbf',\mathbf_j) where \varphi is the kernel function (usually Gaussian), \alpha_j are the variances of the prior on the weight vector w \sim N(0,\alpha^I), and \mathbf_1,\ldots,\mathbf_N are the input vectors of the training set. Compared to that of support vector machines (SVM), the Bayesian formulation of the RVM avoids the set of free parameters of the SVM (that usually require cross-validation-based post-optimizations). However RVMs use an expectation maximization (EM)-like learning method and are therefore at risk of local ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Isotonic Regression
In statistics and numerical analysis, isotonic regression or monotonic regression is the technique of fitting a free-form line to a sequence of observations such that the fitted line is non-decreasing (or non-increasing) everywhere, and lies as close to the observations as possible. Applications Isotonic regression has applications in statistical inference. For example, one might use it to fit an isotonic curve to the means of some set of experimental results when an increase in those means according to some particular ordering is expected. A benefit of isotonic regression is that it is not constrained by any functional form, such as the linearity imposed by linear regression, as long as the function is monotonic increasing. Another application is nonmetric multidimensional scaling, where a low-dimensional embedding for data points is sought such that order of distances between points in the embedding matches order of dissimilarity between points. Isotonic regression is use ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Random Forest
Random forests or random decision forests is an ensemble learning method for classification, regression and other tasks that operates by constructing a multitude of decision trees at training time. For classification tasks, the output of the random forest is the class selected by most trees. For regression tasks, the mean or average prediction of the individual trees is returned. Random decision forests correct for decision trees' habit of overfitting to their training set. Random forests generally outperform decision trees, but their accuracy is lower than gradient boosted trees. However, data characteristics can affect their performance. The first algorithm for random decision forests was created in 1995 by Tin Kam Ho using the random subspace method, which, in Ho's formulation, is a way to implement the "stochastic discrimination" approach to classification proposed by Eugene Kleinberg. An extension of the algorithm was developed by Leo Breiman and Adele Cutler, who reg ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Multilayer Perceptron
A multilayer perceptron (MLP) is a fully connected class of feedforward artificial neural network (ANN). The term MLP is used ambiguously, sometimes loosely to mean ''any'' feedforward ANN, sometimes strictly to refer to networks composed of multiple layers of perceptrons (with threshold activation); see . Multilayer perceptrons are sometimes colloquially referred to as "vanilla" neural networks, especially when they have a single hidden layer. An MLP consists of at least three layers of nodes: an input layer, a hidden layer and an output layer. Except for the input nodes, each node is a neuron that uses a nonlinear activation function. MLP utilizes a supervised learning technique called backpropagation for training. Its multiple layers and non-linear activation distinguish MLP from a linear perceptron. It can distinguish data that is not linearly separable.Cybenko, G. 1989. Approximation by superpositions of a sigmoidal function '' Mathematics of Control, Signals, and Systems'' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calibration (statistics)
There are two main uses of the term calibration in statistics that denote special types of statistical inference problems. "Calibration" can mean :*a reverse process to regression, 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; :*procedures in statistical classification to determine class membership probabilities which assess the uncertainty of a given new observation belonging to each of the already established classes. In addition, "calibration" is used in statistics with the usual general meaning of calibration. For example, model calibration can be also used to refer to Bayesian inference about the value of a model's parameters, given some data set, or more generally to any type of fitting of a statistical model. As Philip Dawid puts it, "a forecaster is ''well calibrated'' if, for example, of those events to which he assign ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Naive Bayes Classifier
In statistics, naive Bayes classifiers are a family of simple "probabilistic classifiers" based on applying Bayes' theorem with strong (naive) independence assumptions between the features (see Bayes classifier). They are among the simplest Bayesian network models, but coupled with kernel density estimation, they can achieve high accuracy levels. Naive Bayes classifiers are highly scalable, requiring a number of parameters linear in the number of variables (features/predictors) in a learning problem. Maximum-likelihood training can be done by evaluating a closed-form expression, which takes linear time, rather than by expensive iterative approximation as used for many other types of classifiers. In the statistics literature, naive Bayes models are known under a variety of names, including simple Bayes and independence Bayes. All these names reference the use of Bayes' theorem in the classifier's decision rule, but naive Bayes is not (necessarily) a Bayesian method. Introductio ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boosting (machine Learning)
In machine learning, boosting is an ensemble meta-algorithm for primarily reducing bias, and also variance in supervised learning, and a family of machine learning algorithms that convert weak learners to strong ones. Boosting is based on the question posed by Kearns and Valiant (1988, 1989):Michael Kearns(1988)''Thoughts on Hypothesis Boosting'' Unpublished manuscript (Machine Learning class project, December 1988) "Can a set of weak learners create a single strong learner?" A weak learner is defined to be a classifier that is only slightly correlated with the true classification (it can label examples better than random guessing). In contrast, a strong learner is a classifier that is arbitrarily well-correlated with the true classification. Robert Schapire's affirmative answer in a 1990 paper to the question of Kearns and Valiant has had significant ramifications in machine learning and statistics, most notably leading to the development of boosting. When first introduced, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Machine Learning (journal)
''Machine Learning'' is a peer-reviewed scientific journal, published since 1986. In 2001, forty editors and members of the editorial board of ''Machine Learning'' resigned in order to support the ''Journal of Machine Learning Research'' (JMLR), saying that in the era of the internet, it was detrimental for researchers to continue publishing their papers in expensive journals with pay-access archives. Instead, they wrote, they supported the model of ''JMLR'', in which authors retained copyright over their papers and archives were freely available on the internet. Following the mass resignation, Kluwer changed their publishing policy to allow authors to self-archive their papers online after peer-review Peer review is the evaluation of work by one or more people with similar competencies as the producers of the work (peers). It functions as a form of self-regulation by qualified members of a profession within the relevant field. Peer review .... Selected articles * * ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Numerical Stability
In the mathematical subfield of numerical analysis, numerical stability is a generally desirable property of numerical algorithms. The precise definition of stability depends on the context. One is numerical linear algebra and the other is algorithms for solving ordinary and partial differential equations by discrete approximation. In numerical linear algebra, the principal concern is instabilities caused by proximity to singularities of various kinds, such as very small or nearly colliding eigenvalues. On the other hand, in numerical algorithms for differential equations the concern is the growth of round-off errors and/or small fluctuations in initial data which might cause a large deviation of final answer from the exact solution. Some numerical algorithms may damp out the small fluctuations (errors) in the input data; others might magnify such errors. Calculations that can be proven not to magnify approximation errors are called ''numerically stable''. One of the common task ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Method In Optimization
In calculus, Newton's method is an iterative method for finding the roots of a differentiable function , which are solutions to the equation . As such, Newton's method can be applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to ), also known as the critical points of . These solutions may be minima, maxima, or saddle points; see section "Several variables" in Critical point (mathematics) and also section "Geometric interpretation" in this article. This is relevant in optimization, which aims to find (global) minima of the function . Newton's method The central problem of optimization is minimization of functions. Let us first consider the case of univariate functions, i.e., functions of a single real variable. We will later consider the more general and more practically useful multivariate case. Given a twice differentiable function f:\mathbb\to \mathbb, we seek to solve the optimization problem : \min_ f(x) . ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
