Declarative Bias in Equation Discovery

Abstract

Declarative bias plays an important role when learning in potentially huge hypothesis spaces. While scientific discovery systems, which perform equation discovery as a subtask, consider such potentially huge hypothesis spaces, few (if any) employ declarative (as opposed to hard-coded) bias to define and restrict their hypothesis space. We present an equation discovery system Lagramge that uses grammars to define and restrict its hypothesis space. These grammars can make use of functions defined as domain specific knowledge, in addition to common mathematical operators. Lagramge was successfully applied to three artificial domains, rediscovering the correct equations. It was also applied to a real-world problem, discovering equations that make sense in terms of domain knowledge and produce accurate predictions. 1 INTRODUCTION The term bias refers to any kind of basis for choosing one generalization over another, other than strict consistency with the observed training examples [Mitchel...