UnivariateIn mathematics, a univariate object is an expression, equation, function or polynomial involving only one variable. Objects involving more than one variable are multivariate. In some cases the distinction between the univariate and multivariate cases is fundamental; for example, the fundamental theorem of algebra and Euclid's algorithm for polynomials are fundamental properties of univariate polynomials that cannot be generalized to multivariate polynomials.
Multivariate random variableIn probability, and statistics, a multivariate random variable or random vector is a list or vector of mathematical variables each of whose value is unknown, either because the value has not yet occurred or because there is imperfect knowledge of its value. The individual variables in a random vector are grouped together because they are all part of a single mathematical system — often they represent different properties of an individual statistical unit.
Singular spectrum analysisIn time series analysis, singular spectrum analysis (SSA) is a nonparametric spectral estimation method. It combines elements of classical time series analysis, multivariate statistics, multivariate geometry, dynamical systems and signal processing. Its roots lie in the classical Karhunen (1946)–Loève (1945, 1978) spectral decomposition of time series and random fields and in the Mañé (1981)–Takens (1981) embedding theorem. SSA can be an aid in the decomposition of time series into a sum of components, each having a meaningful interpretation.
BeamlineIn accelerator physics, a beamline refers to the trajectory of the beam of particles, including the overall construction of the path segment (guide tubes, diagnostic devices) along a specific path of an accelerator facility. This part is either the line in a linear accelerator along which a beam of particles travels, or the path leading from particle generator (e.g. a cyclic accelerator, synchrotron light sources, cyclotrons, or spallation sources) to the experimental end-station.
Particle acceleratorA particle accelerator is a machine that uses electromagnetic fields to propel charged particles to very high speeds and energies, and to contain them in well-defined beams. Large accelerators are used for fundamental research in particle physics. The largest accelerator currently active is the Large Hadron Collider (LHC) near Geneva, Switzerland, operated by the CERN. It is a collider accelerator, which can accelerate two beams of protons to an energy of 6.5 TeV and cause them to collide head-on, creating center-of-mass energies of 13 TeV.
Generative modelIn statistical classification, two main approaches are called the generative approach and the discriminative approach. These compute classifiers by different approaches, differing in the degree of statistical modelling. Terminology is inconsistent, but three major types can be distinguished, following : A generative model is a statistical model of the joint probability distribution on given observable variable X and target variable Y; A discriminative model is a model of the conditional probability of the target Y, given an observation x; and Classifiers computed without using a probability model are also referred to loosely as "discriminative".
Elliptical distributionIn probability and statistics, an elliptical distribution is any member of a broad family of probability distributions that generalize the multivariate normal distribution. Intuitively, in the simplified two and three dimensional case, the joint distribution forms an ellipse and an ellipsoid, respectively, in iso-density plots. In statistics, the normal distribution is used in classical multivariate analysis, while elliptical distributions are used in generalized multivariate analysis, for the study of symmetric distributions with tails that are heavy, like the multivariate t-distribution, or light (in comparison with the normal distribution).
Discriminative modelDiscriminative models, also referred to as conditional models, are a class of logistical models used for classification or regression. They distinguish decision boundaries through observed data, such as pass/fail, win/lose, alive/dead or healthy/sick. Typical discriminative models include logistic regression (LR), conditional random fields (CRFs) (specified over an undirected graph), decision trees, and many others. Typical generative model approaches include naive Bayes classifiers, Gaussian mixture models, variational autoencoders, generative adversarial networks and others.
Bootstrap aggregatingBootstrap aggregating, also called bagging (from bootstrap aggregating), is a machine learning ensemble meta-algorithm designed to improve the stability and accuracy of machine learning algorithms used in statistical classification and regression. It also reduces variance and helps to avoid overfitting. Although it is usually applied to decision tree methods, it can be used with any type of method. Bagging is a special case of the model averaging approach.
