Mediated Uncoupled Learning: Learning Functions without Direct Input-output Correspondences

Ikko Yamane, Junya Honda, Florian Yger, Masashi Sugiyama
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:11637-11647, 2021.

Abstract

Ordinary supervised learning is useful when we have paired training data of input $X$ and output $Y$. However, such paired data can be difficult to collect in practice. In this paper, we consider the task of predicting $Y$ from $X$ when we have no paired data of them, but we have two separate, independent datasets of $X$ and $Y$ each observed with some mediating variable $U$, that is, we have two datasets $S_X = \{(X_i, U_i)\}$ and $S_Y = \{(U’_j, Y’_j)\}$. A naive approach is to predict $U$ from $X$ using $S_X$ and then $Y$ from $U$ using $S_Y$, but we show that this is not statistically consistent. Moreover, predicting $U$ can be more difficult than predicting $Y$ in practice, e.g., when $U$ has higher dimensionality. To circumvent the difficulty, we propose a new method that avoids predicting $U$ but directly learns $Y = f(X)$ by training $f(X)$ with $S_{X}$ to predict $h(U)$ which is trained with $S_{Y}$ to approximate $Y$. We prove statistical consistency and error bounds of our method and experimentally confirm its practical usefulness.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-yamane21a, title = {Mediated Uncoupled Learning: Learning Functions without Direct Input-output Correspondences}, author = {Yamane, Ikko and Honda, Junya and Yger, Florian and Sugiyama, Masashi}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {11637--11647}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/yamane21a/yamane21a.pdf}, url = {https://proceedings.mlr.press/v139/yamane21a.html}, abstract = {Ordinary supervised learning is useful when we have paired training data of input $X$ and output $Y$. However, such paired data can be difficult to collect in practice. In this paper, we consider the task of predicting $Y$ from $X$ when we have no paired data of them, but we have two separate, independent datasets of $X$ and $Y$ each observed with some mediating variable $U$, that is, we have two datasets $S_X = \{(X_i, U_i)\}$ and $S_Y = \{(U’_j, Y’_j)\}$. A naive approach is to predict $U$ from $X$ using $S_X$ and then $Y$ from $U$ using $S_Y$, but we show that this is not statistically consistent. Moreover, predicting $U$ can be more difficult than predicting $Y$ in practice, e.g., when $U$ has higher dimensionality. To circumvent the difficulty, we propose a new method that avoids predicting $U$ but directly learns $Y = f(X)$ by training $f(X)$ with $S_{X}$ to predict $h(U)$ which is trained with $S_{Y}$ to approximate $Y$. We prove statistical consistency and error bounds of our method and experimentally confirm its practical usefulness.} }
Endnote
%0 Conference Paper %T Mediated Uncoupled Learning: Learning Functions without Direct Input-output Correspondences %A Ikko Yamane %A Junya Honda %A Florian Yger %A Masashi Sugiyama %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-yamane21a %I PMLR %P 11637--11647 %U https://proceedings.mlr.press/v139/yamane21a.html %V 139 %X Ordinary supervised learning is useful when we have paired training data of input $X$ and output $Y$. However, such paired data can be difficult to collect in practice. In this paper, we consider the task of predicting $Y$ from $X$ when we have no paired data of them, but we have two separate, independent datasets of $X$ and $Y$ each observed with some mediating variable $U$, that is, we have two datasets $S_X = \{(X_i, U_i)\}$ and $S_Y = \{(U’_j, Y’_j)\}$. A naive approach is to predict $U$ from $X$ using $S_X$ and then $Y$ from $U$ using $S_Y$, but we show that this is not statistically consistent. Moreover, predicting $U$ can be more difficult than predicting $Y$ in practice, e.g., when $U$ has higher dimensionality. To circumvent the difficulty, we propose a new method that avoids predicting $U$ but directly learns $Y = f(X)$ by training $f(X)$ with $S_{X}$ to predict $h(U)$ which is trained with $S_{Y}$ to approximate $Y$. We prove statistical consistency and error bounds of our method and experimentally confirm its practical usefulness.
APA
Yamane, I., Honda, J., Yger, F. & Sugiyama, M.. (2021). Mediated Uncoupled Learning: Learning Functions without Direct Input-output Correspondences. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:11637-11647 Available from https://proceedings.mlr.press/v139/yamane21a.html.

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