Considering Autocorrelation in Predictive Models

Most machine learning, data mining and statistical methods rely on the assumption that the analyzed data points are independent and identically distributed (i.i.d.). More specifically, the individual examples included in the training data are assumed to be drawn independently from each other from the same probability distribution. However, cases where this assumption is violated can be easily found: For example, species are distributed non-randomly across a wide range of spatial scales. The i.i.d. assumption is often violated because of the phenomenon of autocorrelation. The cross-correlation of an attribute with itself is typically referred to as autocorrelation: This is the most general definition found in the literature. Specifically, in spatial analysis, spatial autocorrelation has been defined as the correlation among data values, which is strictly due to the relative location proximity of the objects that the data refer to. It is justified by Tobler’s first law of geography [1] according to which “everything is related to everything else, but near things are more related than distant things”. In network studies, autocorrelation is defined by the homophily principle [2] as the tendency of nodes with similar values to be linked with each other.