Dropout Regularization Versus $\ell_2$-Penalization in the Linear Model

Gabriel Clara; Sophie Langer; Johannes Schmidt-Hieber

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arXiv · 2306.10529

Dropout Regularization Versus $\ell_2$-Penalization in the Linear Model

Gabriel Clara·Sophie Langer·Johannes Schmidt-Hieber

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Abstract

We investigate the statistical behavior of gradient descent iterates with dropout in the linear regression model. In particular, non-asymptotic bounds for the convergence of expectations and covariance matrices of the iterates are derived. The results shed more light on the widely cited connection between dropout and l2-regularization in the linear model. We indicate a more subtle relationship, owing to interactions between the gradient descent dynamics and the additional randomness induced by dropout. Further, we study a simplified variant of dropout which does not have a regularizing effect and converges to the least squares estimator

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Gabriel Clara, Sophie Langer, Johannes Schmidt-Hieber. 2023-06-18. Dropout Regularization Versus $\ell_2$-Penalization in the Linear Model. https://arxiv.org/abs/2306.10529

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