Mean squared errorIn statistics, the mean squared error (MSE) or mean squared deviation (MSD) of an estimator (of a procedure for estimating an unobserved quantity) measures the average of the squares of the errors—that is, the average squared difference between the estimated values and the actual value. MSE is a risk function, corresponding to the expected value of the squared error loss. The fact that MSE is almost always strictly positive (and not zero) is because of randomness or because the estimator does not account for information that could produce a more accurate estimate.
Evolutionary algorithmIn computational intelligence (CI), an evolutionary algorithm (EA) is a subset of evolutionary computation, a generic population-based metaheuristic optimization algorithm. An EA uses mechanisms inspired by biological evolution, such as reproduction, mutation, recombination, and selection. Candidate solutions to the optimization problem play the role of individuals in a population, and the fitness function determines the quality of the solutions (see also loss function).
Stochastic optimizationStochastic optimization (SO) methods are optimization methods that generate and use random variables. For stochastic problems, the random variables appear in the formulation of the optimization problem itself, which involves random objective functions or random constraints. Stochastic optimization methods also include methods with random iterates. Some stochastic optimization methods use random iterates to solve stochastic problems, combining both meanings of stochastic optimization.
Memetic algorithmA memetic algorithm (MA) in computer science and operations research, is an extension of the traditional genetic algorithm (GA) or more general evolutionary algorithm (EA). It may provide a sufficiently good solution to an optimization problem. It uses a suitable heuristic or local search technique to improve the quality of solutions generated by the EA and to reduce the likelihood of premature convergence. Memetic algorithms represent one of the recent growing areas of research in evolutionary computation.
Particle filterParticle filters, or sequential Monte Carlo methods, are a set of Monte Carlo algorithms used to find approximate solutions for filtering problems for nonlinear state-space systems, such as signal processing and Bayesian statistical inference. The filtering problem consists of estimating the internal states in dynamical systems when partial observations are made and random perturbations are present in the sensors as well as in the dynamical system.
Ordinary least squaresIn statistics, ordinary least squares (OLS) is a type of linear least squares method for choosing the unknown parameters in a linear regression model (with fixed level-one effects of a linear function of a set of explanatory variables) by the principle of least squares: minimizing the sum of the squares of the differences between the observed dependent variable (values of the variable being observed) in the input dataset and the output of the (linear) function of the independent variable.
QuantileIn statistics and probability, quantiles are cut points dividing the range of a probability distribution into continuous intervals with equal probabilities, or dividing the observations in a sample in the same way. There is one fewer quantile than the number of groups created. Common quantiles have special names, such as quartiles (four groups), deciles (ten groups), and percentiles (100 groups). The groups created are termed halves, thirds, quarters, etc.
Quantile functionIn probability and statistics, the quantile function outputs the value of a random variable such that its probability is less than or equal to an input probability value. Intuitively, the quantile function associates with a range at and below a probability input the likelihood that a random variable is realized in that range for some probability distribution. It is also called the percentile function (after the percentile), percent-point function or inverse cumulative distribution function (after the cumulative distribution function).
QuartileIn statistics, a quartile is a type of quantile which divides the number of data points into four parts, or quarters, of more-or-less equal size. The data must be ordered from smallest to largest to compute quartiles; as such, quartiles are a form of order statistic. The three main quartiles are as follows: The first quartile (Q1) is defined as the middle number between the smallest number (minimum) and the median of the data set. It is also known as the lower quartile, as 25% of the data is below this point.
Set theorySet theory is the branch of mathematical logic that studies sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory, as a branch of mathematics, is mostly concerned with those that are relevant to mathematics as a whole. The modern study of set theory was initiated by the German mathematicians Richard Dedekind and Georg Cantor in the 1870s. In particular, Georg Cantor is commonly considered the founder of set theory.
Set (mathematics)A set is the mathematical model for a collection of different things; a set contains elements or members, which can be mathematical objects of any kind: numbers, symbols, points in space, lines, other geometrical shapes, variables, or even other sets. The set with no element is the empty set; a set with a single element is a singleton. A set may have a finite number of elements or be an infinite set. Two sets are equal if they have precisely the same elements. Sets are ubiquitous in modern mathematics.
Q–Q plotIn statistics, a Q–Q plot (quantile-quantile plot) is a probability plot, a graphical method for comparing two probability distributions by plotting their quantiles against each other. A point (x, y) on the plot corresponds to one of the quantiles of the second distribution (y-coordinate) plotted against the same quantile of the first distribution (x-coordinate). This defines a parametric curve where the parameter is the index of the quantile interval.
