Comparing Two Counting Methods for Estimating the Probabilities of Strings

There are two methods for counting the number of occurrences of a string in another large string. One is to count the number of places where the string is found. The other is to determine how many pieces of string can be extracted without overlapping. The difference between the two becomes apparent when the string is part of a periodic pattern. This research reports that the difference is significant in estimating the occurrence probability of a pattern. In this study, the strings used in the experiments are approximated from time-series data. The task involves classifying strings by estimating the probability or computing the information quantity. First, the frequencies of all substrings of a string are computed. Each counting method may sometimes produce different frequencies for an identical string. Second, the probability of the most probable segmentation is selected. The probability of the string is the product of all probabilities of substrings in the selected segmentation. The classification results demonstrate that the difference in counting methods is statistically significant, and that the method without overlapping is better.