Practical Algorithms for Pattern Based Linear Regression

We consider the problem of discovering the optimal pattern from a set of strings and associated numeric attribute values. The goodness of a pattern is measured by the correlation between the number of occurrences of the pattern in each string, and the numeric attribute value assigned to the string. We present two algorithms based on suffix trees, that can find the optimal substring pattern in O(Nn) and O(N) time, respectively, where n is the number of strings and N is their total length. We further present a general branch and bound strategy that can be used when considering more complex pattern classes. We also show that combining the O(N) algorithm and the branch and bound heuristic increases the efficiency of the algorithm considerably.