Unified Analysis of Continuous Weak Features Learning with Applications to Learning from Missing Data

Kosuke Sugiyama, Masato Uchida
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:57270-57310, 2025.

Abstract

This paper addresses weak features learning (WFL), focusing on learning scenarios characterized by low-quality input features (weak features; WFs) that arise due to missingness, measurement errors, or ambiguous observations. We present a theoretical formalization and error analysis of WFL for continuous WFs (continuous WFL), which has been insufficiently explored in existing literature. A previous study established formalization and error analysis for WFL with discrete WFs (discrete WFL); however, this analysis does not extend to continuous WFs due to the inherent constraints of discreteness. To address this, we propose a theoretical framework specifically designed for continuous WFL, systematically capturing the interactions between feature estimation models for WFs and label prediction models for downstream tasks. Furthermore, we derive the theoretical conditions necessary for both sequential and iterative learning methods to achieve consistency. By integrating the findings of this study on continuous WFL with the existing theory of discrete WFL, we demonstrate that the WFL framework is universally applicable, providing a robust theoretical foundation for learning with low-quality features across diverse application domains.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-sugiyama25b, title = {Unified Analysis of Continuous Weak Features Learning with Applications to Learning from Missing Data}, author = {Sugiyama, Kosuke and Uchida, Masato}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {57270--57310}, 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/sugiyama25b/sugiyama25b.pdf}, url = {https://proceedings.mlr.press/v267/sugiyama25b.html}, abstract = {This paper addresses weak features learning (WFL), focusing on learning scenarios characterized by low-quality input features (weak features; WFs) that arise due to missingness, measurement errors, or ambiguous observations. We present a theoretical formalization and error analysis of WFL for continuous WFs (continuous WFL), which has been insufficiently explored in existing literature. A previous study established formalization and error analysis for WFL with discrete WFs (discrete WFL); however, this analysis does not extend to continuous WFs due to the inherent constraints of discreteness. To address this, we propose a theoretical framework specifically designed for continuous WFL, systematically capturing the interactions between feature estimation models for WFs and label prediction models for downstream tasks. Furthermore, we derive the theoretical conditions necessary for both sequential and iterative learning methods to achieve consistency. By integrating the findings of this study on continuous WFL with the existing theory of discrete WFL, we demonstrate that the WFL framework is universally applicable, providing a robust theoretical foundation for learning with low-quality features across diverse application domains.} }
Endnote
%0 Conference Paper %T Unified Analysis of Continuous Weak Features Learning with Applications to Learning from Missing Data %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-sugiyama25b %I PMLR %P 57270--57310 %U https://proceedings.mlr.press/v267/sugiyama25b.html %V 267 %X This paper addresses weak features learning (WFL), focusing on learning scenarios characterized by low-quality input features (weak features; WFs) that arise due to missingness, measurement errors, or ambiguous observations. We present a theoretical formalization and error analysis of WFL for continuous WFs (continuous WFL), which has been insufficiently explored in existing literature. A previous study established formalization and error analysis for WFL with discrete WFs (discrete WFL); however, this analysis does not extend to continuous WFs due to the inherent constraints of discreteness. To address this, we propose a theoretical framework specifically designed for continuous WFL, systematically capturing the interactions between feature estimation models for WFs and label prediction models for downstream tasks. Furthermore, we derive the theoretical conditions necessary for both sequential and iterative learning methods to achieve consistency. By integrating the findings of this study on continuous WFL with the existing theory of discrete WFL, we demonstrate that the WFL framework is universally applicable, providing a robust theoretical foundation for learning with low-quality features across diverse application domains.
APA
Sugiyama, K. & Uchida, M.. (2025). Unified Analysis of Continuous Weak Features Learning with Applications to Learning from Missing Data. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:57270-57310 Available from https://proceedings.mlr.press/v267/sugiyama25b.html.

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