Linear regression with partially mismatched data: local search with theoretical guarantees

Abstract Linear regression is a fundamental modeling tool in statistics and related fields. In this paper, we study an important variant of linear which the predictor-response pairs are partially mismatched. We use optimization formulation to simultaneously learn underlying coefficients permutation corresponding mismatches. The combinatorial structure problem leads computational challenges. propose simple greedy local search algorithm for that enjoys strong theoretical guarantees appealing performance. prove under suitable scaling number mismatched compared samples features, certain assumptions on data; our converges nearly-optimal solution at rate. particular, noiseless case, global optimal with convergence Based result, upper bound estimation error parameter. also approximate step allows us scale approach much larger instances. conduct numerical experiments gather further insights into results, show promising performance gains existing approaches.