Learning Interpretable Classification Rules with Boolean Compressed Sensing

An important problem in the context of supervised machine learning is designing systems which are interpretable by humans. In domains such as law, medicine, and finance that deal with human lives, delegating the decision to a black-box machine-learning model carries significant operational risk, and often legal implications, thus requiring interpretable classifiers. Building on ideas from Boolean compressed sensing, we propose a rule-based classifier which explicitly balances accuracy versus interpretability in a principled optimization formulation. We represent the problem of learning conjunctive clauses or disjunctive clauses as an adaptation of a classical problem from statistics, Boolean group testing, and apply a novel linear programming (LP) relaxation to find solutions. We derive theoretical results for recovering sparse rules which parallel the conditions for exact recovery of sparse signals in the compressed sensing literature. This is an exciting development in interpretable learning where most prior work has focused on heuristic solutions. We also consider a more general class of rule-based classifiers, checklists and scorecards, learned using ideas from threshold group testing. We show competitive classification accuracy using the proposed approach on real-world data sets.