finds this relationship for the calibration interval, the relationship is then typically used to extrapolate the same relationship into a subsequent validation interval during which the predictive power can be tested. Machine learning algorithms can be appropriate for situations where data concerning pattern are available and theory concerning process is scant. There are many cases where it is possible to obtain land cover maps from more than one time point along with explanatory variables for a study site where the investigator is partially ignorant concerning the detailed processes of land transformation. A machine learning algorithm attempts to learn the mathematical or logical relationships among the patterns of land cover and the patterns of the explanatory variables. The machine learning algorithm focuses exclusively on encoding and extrapolating the pattern of the land change, as opposed to the process of change. If the approach is used for prediction, then the prediction assumes stationarity in the land change pattern from the calibration interval to the subsequent time interval. Machine learning algorithms are used to predict by extrapolating historic patterns and can perform the extrapolation in a manner that does not require theory concerning detailed processes of change.

Machine learning algorithms are not designed to simulate feedbacks and nonstationary processes in coupled natural and human systems, nor are they designed to evaluate the effects of policies that attempt to modify processes so that future patterns will be different than the past patterns. Machine learning algorithms are not designed to simulate the mechanisms of human decision making, because machine learning algorithms lack theory concerning the behavior of decision making.

Statistical regression methods assume a fixed mathematical form with coefficients that an algorithm estimates to produce an optimal fit, where optimal is defined by a mathematical criterion, i.e., a maximum-likelihood criterion. The maximum-likelihood criterion leads to a mathematical formula to estimate the regression’s coefficients. For example, the regression equation could assume a monotonic sigmoidal relationship between land cover change and topographic slope. Then the maximum-likelihood algorithm estimates the equation’s coefficients so the regression curve fits as closely as possible to the data, given the form of the monotonic sigmoidal relationship. The coefficients indicate whether the assumed monotonic relationships are increasing or decreasing, and at what rate. The logistic regression might also include interactions among the explanatory variables. Diagnostic measurements help to interpret the fitted coefficients of the regression equation.

In comparison with logistic regression, machine learning algorithms do not require strong assumptions concerning a particular form of a mathematical equation to express a relationship between the land cover map(s) and the map(s) of explanatory variable(s). Machine learning algorithms attempt to mimic biological learning systems through predictive artificial intelligence tools. They fit a relationship between the land change variable and the explanatory variable(s)



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