Debiasing Stochastic Gradient Descent to handle missing values

Aude Sportisse (1) , Claire Boyer (2, 1) , Aymeric Dieuleveut (3) , Julie Josse (3, 4)

1 LPSM (UMR_8001) - Laboratoire de Probabilités, Statistique et Modélisation
2 DMA - Département de Mathématiques et Applications - ENS Paris
3 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
4 XPOP - Modélisation en pharmacologie de population

Stochastic gradient algorithm is a key ingredient of many machine learning methods, particularly appropriate for large-scale learning.However, a major caveat of large data is their incompleteness.We propose an averaged stochastic gradient algorithm handling missing values in linear models. This approach has the merit to be free from the need of any data distribution modeling and to account for heterogeneous missing proportion.In both streaming and finite-sample settings, we prove that this algorithm achieves convergence rate of $\mathcal{O}(\frac{1}{n})$ at the iteration $n$, the same as without missing values. We show the convergence behavior and the relevance of the algorithm not only on synthetic data but also on real data sets, including those collected from medical register.

Mots clés: Stochastic approximation; Optimization; Missing data; Supervised learning

Domaines: Statistiques [math.ST]

Aude Sportisse, Claire Boyer, Aymeric Dieuleveut, Julie Josse. Debiasing Stochastic Gradient Descent to handle missing values. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver, Canada. ⟨hal-02483651v2⟩