Multiple change-point detection with a genetic algorithm

Abstract

A common change-point problem is considered where the population mean of a random variable is suspected of undergoing abrupt changes in course of a time series. It is usual in practice that no information on positions or number of such shifts is available beforehand. Finding the change points, i.e. the positions of the shifts, in such a situation is a delicate statistical problem since any considered sample may actually represent a mixture of two or more populations where values from both sides of a yet unrecognized change point are unconsciously assembled. If this is the case, underlying assumptions of an employed statistical two-sample test are usually violated. Consequently, no de®nite decision should be based on just one value of the test statistic. Such a value is rather, as a precaution, to be regarded as an only approximate indicator of the quality of a hypothesis about change-point positions. Given these conclusions, it is found imperative to treat the problem of multiple change-point detection as one of global optimization. A cost function is constructed in such a manner that the change-point con®guration yielding the global optimum is compliant with statisticaltheoretical requirements to the utmost extent. The used advanced optimization tool, a genetic algorithm, is both ef®cient ± as it takes advantage of the information about promising change-point positions encountered in previously investigated trial con®gurations ± and¯exible (as it is open to any modi®cation of the change-point con®gu-ration at any time). Experiments using numerical simulation con®rm adequate performance of the method in an application where a common change-point detection procedure based on Student's two-sample t-test is used to detect an arbitrary number of shifts in the mean of a normally distributed random variable.

Genetic algorithms for outlier detection and variable selection in linear regression models

“…Unfortunately, however, in many cases the estimation of the models is considerably more costly in CPU time, which perhaps limits the practical applicability of the method somewhat. One further point, not deemed to be of sufficient interest to be tackled here, is the fact that exactly the same models are estimated several times during the run of the GA. One possibility to circumvent this is to keep track of all the models that have already been considered, and estimate each model only once, as in [11]. If the estimation of the models were more time-consuming, this would clearly be worth considering.…”

“…In addition to variable selection and outlier detection, similar GAs could be built to simultaneously consider also other kinds of modeling choices. These could include, for example, the detection of change-points in time series models, as in [11].…”

“…If such models are considered for a time series, there exists a large number of potential model forms, and finding the best one using conventional methods may require the estimation of a prohibitive number of models. [11] describes a GA for the detection of multiple change-points (or level shifts) in a time series. The problems caused by changepoints are similar to those caused by outliers, in that the detection of one change-point affects the consequent detection of further change-points.…”

Genetic algorithms for outlier detection in multiple regression with different information criteria

“…The GAs are used in the diagnostics as evaluation functions to drive the search for good subsets. Jann [37] describes GAs for the detection of level shifts in a time series. Ishibuchi et al [38] used GAs for the feature selection in data mining and they gave a lot of references about this literature.…”

Identifying the time of a step change in bivariate binomial processes

“…For example, Jann [4] developed an estimator for multiple changes using genetic algorithm or Ghazanfari et al [5] applied clustering method for change point estimation in Shewhart control charts, and Atashgar and Noorossana [6] used artificial neural network for this purpose.…”