Information Geometric Perspective of Modal Linear Regression

  • Keishi Sando
  • Shotaro Akaho
  • Noboru Murata
  • Hideitsu HinoEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11303)


Modal linear regression (MLR) is a standard method for modeling the conditional mode of a response variable using a linear combination of explanatory variables. It is effective when dealing with response variables with an asymmetric, multi-modal distribution. Because of the nonparametric nature of MLR, it is difficult to construct a statistical model manifold in the sense of information geometry. In this work, a model manifold is constructed using observations instead of explicit parametric models. We also propose a method for constructing a data manifold based on an empirical distribution. 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.


Modal linear regression Information geometry EM algorithm 


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  1. 1.The Institute of Statistical MathematicsTachikawaJapan
  2. 2.University of TsukubaTsukubaJapan
  3. 3.National Institute of Advanced Industrial Science and TechnologyTsukubaJapan
  4. 4.Waseda UniversityShinjukuJapan

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