Learning CNF Theories Using MDL and Predicate Invention

We revisit the problem of learning logical theories from examples, one of the most quintessential problems in machine learning. More specifically, we develop an approach to learn CNF-formulae from satisfiability. This is a setting in which the examples correspond to partial interpretations and an example is classified as positive when it is logically consistent with the theory. We present a novel algorithm, called Mistle -- Minimal SAT Theory Learner, for learning such theories. The distinguishing features are that 1) Mistle performs predicate invention and inverse resolution, 2) is based on the MDL principle to compress the data, and 3) combines this with frequent pattern mining to find the most interesting theories. The experiments demonstrate that Mistle can learn CNF theories accurately and works well in tasks involving compression and classification.

Estimation of the Time-Dependent Profile of a Melting Front by Inverse Resolution

The profile and time evolution of a solid/liquid interface in a phase change process is estimated by solving an inverse heat transfer problem, using data measurements in the solid phase only. One then faces the inverse resolution of a heat equation in a variable and a priori unknown 2D domain. This ill-posed problem is solved by a regularization approach: the unknown function (position of the melting front) is obtained by minimization of a two component criterion, consisting of a distance between the output of a simulation model and the measured data, to which a penalizing function is added in order to restore the continuity of the inverse operator. A numerical study is developed to analyze the validity domain of the identification method. From simulation tests, it is shown that the minimum signal/noise ratio that can be handled depends strongly on the position of the measurement sensors.