A Unified Framework for Generalization Error Analysis of Learning with Arbitrary Discrete Weak Features

Kosuke Sugiyama, Masato Uchida
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:57249-57269, 2025.

Abstract

In many real-world applications, predictive tasks inevitably involve low-quality input features (Weak Features; WFs) which arise due to factors such as misobservations, missingness, or partial observations. While several methods have been proposed to estimate the true values of specific types of WFs and to solve a downstream task, a unified theoretical framework that comprehensively addresses these methods remains underdeveloped. In this paper, we propose a unified framework called Weak Features Learning (WFL), which accommodates arbitrary discrete WFs and a broad range of learning algorithms, and we demonstrate its validity. Furthermore, we introduce a class of algorithms that learn both the estimation model for WFs and the predictive model for a downstream task and perform a generalization error analysis under finite-sample conditions. Our results elucidate the interdependencies between the estimation errors of WFs and the prediction error of a downstream task, as well as the theoretical conditions necessary for the learning approach to achieve consistency. This work establishes a unified theoretical foundation, providing generalization error analysis and performance guarantees, even in scenarios where WFs manifest in diverse forms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-sugiyama25a, title = {A Unified Framework for Generalization Error Analysis of Learning with Arbitrary Discrete Weak Features}, author = {Sugiyama, Kosuke and Uchida, Masato}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {57249--57269}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/sugiyama25a/sugiyama25a.pdf}, url = {https://proceedings.mlr.press/v267/sugiyama25a.html}, abstract = {In many real-world applications, predictive tasks inevitably involve low-quality input features (Weak Features; WFs) which arise due to factors such as misobservations, missingness, or partial observations. While several methods have been proposed to estimate the true values of specific types of WFs and to solve a downstream task, a unified theoretical framework that comprehensively addresses these methods remains underdeveloped. In this paper, we propose a unified framework called Weak Features Learning (WFL), which accommodates arbitrary discrete WFs and a broad range of learning algorithms, and we demonstrate its validity. Furthermore, we introduce a class of algorithms that learn both the estimation model for WFs and the predictive model for a downstream task and perform a generalization error analysis under finite-sample conditions. Our results elucidate the interdependencies between the estimation errors of WFs and the prediction error of a downstream task, as well as the theoretical conditions necessary for the learning approach to achieve consistency. This work establishes a unified theoretical foundation, providing generalization error analysis and performance guarantees, even in scenarios where WFs manifest in diverse forms.} }
Endnote
%0 Conference Paper %T A Unified Framework for Generalization Error Analysis of Learning with Arbitrary Discrete Weak Features %A Kosuke Sugiyama %A Masato Uchida %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-sugiyama25a %I PMLR %P 57249--57269 %U https://proceedings.mlr.press/v267/sugiyama25a.html %V 267 %X In many real-world applications, predictive tasks inevitably involve low-quality input features (Weak Features; WFs) which arise due to factors such as misobservations, missingness, or partial observations. While several methods have been proposed to estimate the true values of specific types of WFs and to solve a downstream task, a unified theoretical framework that comprehensively addresses these methods remains underdeveloped. In this paper, we propose a unified framework called Weak Features Learning (WFL), which accommodates arbitrary discrete WFs and a broad range of learning algorithms, and we demonstrate its validity. Furthermore, we introduce a class of algorithms that learn both the estimation model for WFs and the predictive model for a downstream task and perform a generalization error analysis under finite-sample conditions. Our results elucidate the interdependencies between the estimation errors of WFs and the prediction error of a downstream task, as well as the theoretical conditions necessary for the learning approach to achieve consistency. This work establishes a unified theoretical foundation, providing generalization error analysis and performance guarantees, even in scenarios where WFs manifest in diverse forms.
APA
Sugiyama, K. & Uchida, M.. (2025). A Unified Framework for Generalization Error Analysis of Learning with Arbitrary Discrete Weak Features. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:57249-57269 Available from https://proceedings.mlr.press/v267/sugiyama25a.html.

Related Material