Information geometry of modal linear regression

Modal linear regression (MLR) is used for modeling the conditional mode of a response as a linear predictor of explanatory variables. It is an effective approach to dealing with response variables having a multimodal distribution or those contaminated by outliers. Because of the semiparametric nature of MLR, constructing a statistical model manifold is difficult with the conventional approach. To overcome this difficulty, we first consider the information geometric perspective of the modal expectation–maximization (EM) algorithm. Based on this perspective, model manifolds for MLR are constructed according to observations, and a data manifold is constructed based on the empirical distribution. In this paper, the em algorithm, which is a geometric formulation of the EM algorithm, of MLR is shown to be equivalent to the conventional EM algorithm of MLR. The robustness of the MLR model is also discussed in terms of the influence function and information geometry.