Pattern Discovery as Event Association

A basic task of machine learning and data mining is to automatically uncover patterns that reflect regularities in a data set. When dealing with a large database, especially when domain knowledge is not available or very weak, this can be a challenging task. The purpose of pattern discovery is to find non-random relations among events from data sets. For example, the “exclusive OR” (XOR) problem concerns 3 binary variables, A, B and C=A⊗B, i.e. C is true when either A or B, but not both, is true. Suppose not knowing that it is the XOR problem, we would like to check whether or not the occurrence of the compound event [A=T, B=T, C=F] is just a random happening. If we could estimate its frequency of occurrences under the random assumption, then we know that it is not random if the observed frequency deviates significantly from that assumption. We refer to such a compound event as an event association pattern, or simply a pattern, if its frequency of occurrences significantly deviates from the default random assumption in the statistical sense. For instance, suppose that an XOR database contains 1000 samples and each primary event (e.g. [A=T]) occurs 500 times. The expected frequency of occurrences of the compound event [A=T, B=T, C=F] under the independence assumption is 0.5×0.5×0.5×1000 = 125. Suppose that its observed frequency is 250, we would like to see whether or not the difference between the observed and expected frequencies (i.e. 250 – 125) is significant enough to indicate that the compound event is not a random happening. Andrew K. C. Wong University of Waterloo, Canada