Linear predictor on linearly-generated data with missing values: non consistency and solutions

Abstract : We consider building predictors when the data have missing values. We study the seemingly-simple case where the target to predict is a linear function of the fully-observed data and we show that, in the presence of missing values, the optimal predictor may not be linear. In the particular Gaussian case, it can be written as a linear function of multiway interactions between the observed data and the various missing-value indicators. Due to its intrinsic complexity, we study a simple approximation and prove generalization bounds with finite samples, highlighting regimes for which each method performs best. We then show that multilayer perceptrons with ReLU activation functions can be consistent, and can explore good trade-offs between the true model and approximations. Our study highlights the interesting family of models that are beneficial to fit with missing values depending on the amount of data available.
Document type :
Preprints, Working Papers, ...
Complete list of metadatas

https://hal.archives-ouvertes.fr/hal-02464569
Contributor : Marine Le Morvan <>
Submitted on : Monday, February 3, 2020 - 12:11:14 PM
Last modification on : Monday, February 10, 2020 - 6:14:19 PM

Files

main.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-02464569, version 1
  • ARXIV : 2002.00658

Citation

Marine Le Morvan, Nicolas Prost, Julie Josse, Erwan Scornet, Gaël Varoquaux. Linear predictor on linearly-generated data with missing values: non consistency and solutions. 2020. ⟨hal-02464569⟩

Share

Metrics

Record views

70

Files downloads

38