2022-06-28-ayme22a.md

title	booktitle	abstract	layout	series	publisher	issn	id	month	tex_title	firstpage	lastpage	page	order	cycles	bibtex_author	author	date	address	container-title	volume	genre	issued	pdf	extras
Near-optimal rate of consistency for linear models with missing values	Proceedings of the 39th International Conference on Machine Learning	Missing values arise in most real-world data sets due to the aggregation of multiple sources and intrinsically missing information (sensor failure, unanswered questions in surveys...). In fact, the very nature of missing values usually prevents us from running standard learning algorithms. In this paper, we focus on the extensively-studied linear models, but in presence of missing values, which turns out to be quite a challenging task. Indeed, the Bayes predictor can be decomposed as a sum of predictors corresponding to each missing pattern. This eventually requires to solve a number of learning tasks, exponential in the number of input features, which makes predictions impossible for current real-world datasets. First, we propose a rigorous setting to analyze a least-square type estimator and establish a bound on the excess risk which increases exponentially in the dimension. Consequently, we leverage the missing data distribution to propose a new algorithm, and derive associated adaptive risk bounds that turn out to be minimax optimal. Numerical experiments highlight the benefits of our method compared to state-of-the-art algorithms used for predictions with missing values.	inproceedings	Proceedings of Machine Learning Research	PMLR	2640-3498	ayme22a	0	Near-optimal rate of consistency for linear models with missing values	1211	1243	1211-1243	1211	false	Ayme, Alexis and Boyer, Claire and Dieuleveut, Aymeric and Scornet, Erwan	given family Alexis Ayme given family Claire Boyer given family Aymeric Dieuleveut given family Erwan Scornet	2022-06-28		Proceedings of the 39th International Conference on Machine Learning	162	inproceedings	date-parts 2022 6 28	https://proceedings.mlr.press/v162/ayme22a/ayme22a.pdf