Application of the method of maximum entropy in the mean to classification problems

• The classification problem appears in a large variety of fields.
• It can be regarded to be linear inverse problem with convex constraints and data in sets.
• An important version of the problem appears in the context of credit scoring.
• The problem can be solved efficiently with the method of maximum entropy in the mean.
• The solution obtained with MEM competes favorably when compared to standard methods like SVM and kNN.

In this note we propose an application of the method of maximum entropy in the mean to solve a class of inverse problems comprising classification problems and feasibility problems appearing in optimization. Such problems may be thought of as linear inverse problems with convex constraints imposed on the solution as well as on the data. The method of maximum entropy in the mean proves to be a very useful tool to deal with this type of problems.