{{unreferenced, date=June 2012 In

mathematical modeling A mathematical model is a description of a system using mathematical concepts and language. The process of developing a mathematical model is termed mathematical modeling. Mathematical models are used in the natural sciences (such as physics, ...

, a guess value is more commonly called a starting value or initial value. These are necessary for most

optimization Mathematical optimization (alternatively spelled ''optimisation'') or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfi ...

problems which use

search algorithms In computer science, a search algorithm is an algorithm designed to solve a search problem. Search algorithms work to retrieve information stored within particular data structure, or calculated in the search space of a problem domain, with eith ...

, because those algorithms are mainly

deterministic Determinism is a philosophical view, where all events are determined completely by previously existing causes. Deterministic theories throughout the history of philosophy have developed from diverse and sometimes overlapping motives and consi ...

and

iterative Iteration is the repetition of a process in order to generate a (possibly unbounded) sequence of outcomes. Each repetition of the process is a single iteration, and the outcome of each iteration is then the starting point of the next iteration. ...

, and they need to start somewhere. One common type of application is

nonlinear regression In statistics, nonlinear regression is a form of regression analysis in which observational data are modeled by a function which is a nonlinear combination of the model parameters and depends on one or more independent variables. The data are fi ...

Use

The quality of the initial values can have a considerable impact on the success or lack of such of the search algorithm. This is because the

fitness function {{no footnotes, date=May 2015 A fitness function is a particular type of objective function that is used to summarise, as a single figure of merit, how close a given design solution is to achieving the set aims. Fitness functions are used in genet ...

objective function In mathematical optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one or more variables onto a real number intuitively representing some "cos ...

(in many cases a sum of squared errors ( SSE)) can have difficult shapes. In some parts of the search region, the function may increase exponentially, in others quadratically, and there may be regions where the function

asymptotes In analytic geometry, an asymptote () of a curve is a line such that the distance between the curve and the line approaches zero as one or both of the ''x'' or ''y'' coordinates tends to infinity. In projective geometry and related contexts, ...

to a

plateau In geology and physical geography, a plateau (; ; ), also called a high plain or a tableland, is an area of a highland consisting of flat terrain that is raised sharply above the surrounding area on at least one side. Often one or more sides ...

. Starting values that fall in an exponential region can lead to algorithm failure because of

arithmetic overflow Arithmetic () is an elementary part of mathematics that consists of the study of the properties of the traditional operations on numbers—addition, subtraction, multiplication, division, exponentiation, and extraction of roots. In the 19th ...

. Starting values that fall in the asymptotic plateau region can lead to algorithm failure because of "

dithering Dither is an intentionally applied form of noise used to randomize quantization error, preventing large-scale patterns such as color banding in images. Dither is routinely used in processing of both digital audio and video data, and is ofte ...

". Deterministic search algorithms may use a slope function to go to a minimum. If the slope is very small, then underflow errors can cause the algorithm to wander, seemingly aimlessly; this is dithering.

Finding value

Guess values can be determined a number of ways. Guessing is one of them. If one is familiar with the type of problem, then this is an educated guess or

guesstimate ''Guesstimate'' is an informal English portmanteau of ''guess'' and ''estimate'', first used by American statisticians in 1934 or 1935.linearization In mathematics, linearization is finding the linear approximation to a function at a given point. The linear approximation of a function is the first order Taylor expansion around the point of interest. In the study of dynamical systems, linea ...

, solving

simultaneous equations In mathematics, a set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought. An equation system is usually classified in the same manner as single ...

, reducing

dimensions In physics and mathematics, the dimension of a mathematical space (or object) is informally defined as the minimum number of coordinates needed to specify any point within it. Thus, a line has a dimension of one (1D) because only one coord ...

, treating the problem as a

time series In mathematics, a time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. E ...

, converting the problem to a (hopefully)

linear Linearity is the property of a mathematical relationship ('' function'') that can be graphically represented as a straight line. Linearity is closely related to '' proportionality''. Examples in physics include rectilinear motion, the linear ...

differential equation In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, a ...

, and using

mean There are several kinds of mean in mathematics, especially in statistics. Each mean serves to summarize a given group of data, often to better understand the overall value ( magnitude and sign) of a given data set. For a data set, the '' ari ...

values. Further methods for determining starting values and optimal values in their own right come from

stochastic Stochastic (, ) refers to the property of being well described by a random probability distribution. Although stochasticity and randomness are distinct in that the former refers to a modeling approach and the latter refers to phenomena themselve ...

methods, the most commonly known of these being

evolutionary algorithms In 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 reprod ...

and particularly

genetic algorithms In computer science and operations research, a genetic algorithm (GA) is a metaheuristic inspired by the process of natural selection that belongs to the larger class of evolutionary algorithms (EA). Genetic algorithms are commonly used to gene ...

. Mathematical optimization Regression analysis Computational statistics