Theoretical and Experimental Study of a Complexity Measure for Analogical Transfer

Fadi Badra, Marie-Jeanne Lesot, Aman Barakat, Christophe Marsala

Abstract: Analogical transfer addresses classification and regression tasks, performing a plausible inference according to which similar instances are likely to be associated with similar labels. This paper proposes a detailed study of the ordinal implementation of this principle by the so-called $${\texttt {CoAT}}$$ algorithm, that is based on a data set complexity measure quantifying the number of inversions observed when ranking the data according to their instance or label similarities. At a theoretical level, it establishes an upper bound of the complexity measure, providing a reference value to which the observed one can be compared. At an algorithmic level, it proposes an optimization that allows decreasing the computational complexity by one order of magnitude. At an experimental level, it studies the correlation of the complexity measure with the accuracy of the conducted label inference, as well as with the classification task difficulty, as captured by the class overlapping degree.