Abstract
We discuss an information-geometric framework for a regression model, in which the regression function accompanies with the predictor function and the conditional density function. We introduce the e-geodesic and m-geodesic on the space of all predictor functions, of which the pair leads to the Pythagorean identity for a right triangle spinned by the two geodesics. Further, a statistical modeling to combine predictor functions in a nonlinear fashion is discussed by generalized average, and in particular, we observe the flexible property of the log-exp average.
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Eguchi, S., Omae, K. (2017). Information Geometry of Predictor Functions in a Regression Model. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_65
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DOI: https://doi.org/10.1007/978-3-319-68445-1_65
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