Abstract
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.
Supported by JST KAKENHI 16K16108, 17H01793 and JST CREST JPMJCR1761.
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Sando, K., Akaho, S., Murata, N., Hino, H. (2018). Information Geometric Perspective of Modal Linear Regression. In: Cheng, L., Leung, A., Ozawa, S. (eds) Neural Information Processing. ICONIP 2018. Lecture Notes in Computer Science(), vol 11303. Springer, Cham. https://doi.org/10.1007/978-3-030-04182-3_47
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DOI: https://doi.org/10.1007/978-3-030-04182-3_47
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