TY - GEN
T1 - Information geometric perspective of modal linear regression
AU - Sando, Keishi
AU - Akaho, Shotaro
AU - Murata, Noboru
AU - Hino, Hideitsu
N1 - Funding Information:
Supported by JST KAKENHI 16K16108, 17H01793 and JST CREST JPMJCR1761.
Publisher Copyright:
© Springer Nature Switzerland AG 2018.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - EM algorithm
KW - Information geometry
KW - Modal linear regression
UR - http://www.scopus.com/inward/record.url?scp=85059008645&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85059008645&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-04182-3_47
DO - 10.1007/978-3-030-04182-3_47
M3 - Conference contribution
AN - SCOPUS:85059008645
SN - 9783030041816
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 535
EP - 545
BT - Neural Information Processing - 25th International Conference, ICONIP 2018, Proceedings
A2 - Cheng, Long
A2 - Ozawa, Seiichi
A2 - Leung, Andrew Chi Sing
PB - Springer Verlag
T2 - 25th International Conference on Neural Information Processing, ICONIP 2018
Y2 - 13 December 2018 through 16 December 2018
ER -