Изотондық регрессия: сандық талдау әдісі

Type of numerical analysis

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.

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 used iteratively to fit ideal distances to preserve relative dissimilarity order. Isotonic regression is also used in probabilistic classification to calibrate the predicted probabilities of supervised machine learning models. Isotonic regression for the simply ordered case with univariate has been applied to estimating continuous dose response relationships in fields such as anesthesiology and toxicology. Narrowly speaking, isotonic regression only provides point estimates at observed values of Estimation of the complete dose response curve without any additional assumptions is usually done via linear interpolation between the point estimates. Software for computing isotone (monotonic) regression has been developed for R, Stata, and Python.