Combining Logical Abduction and Statistical Induction: Discovering Written Primitives with Human Knowledge.

In many real tasks there are human knowledge expressed in logic formulae as well as data samples described by raw features (e.g., pixels, strings). It is popular to apply SRL or PILP techniques to exploit human knowledge through learning of symbolic data, or statistical learning techniques to learn from the raw data samples; however, it is often desired to directly exploit these logic formulae on raw data processing, like human beings utilizing knowledge to guide perception. In this paper, we propose an approach, LASIN, which combines Logical Abduction and Statistical INduction. The LASIN approach generates candidate hypotheses based on the abduction of first-order formulae, and then, the hypotheses are exploited as constraints for statistical induction. We apply the LASIN approach to the learning of representation of written primitives, where a primitive is a basic component in human writing. Our results show that the discovered primitives are reasonable for human perception, and these primitives, if used in learning tasks such as classification and domain adaptation, lead to better performances than simply applying feature learning based on raw data only.