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Generalization Error of Generalized Linear Models in High Dimensions

Melikasadat Emami · Mojtaba Sahraee-Ardakan · Parthe Pandit · Sundeep Rangan · Alyson Fletcher

Keywords: [ Information Theory and Estimation ] [ Supervised Learning ]


At the heart of machine learning lies the question of generalizability of learned rules over previously unseen data.
While over-parameterized models based on neural networks are now ubiquitous in machine learning applications, our understanding of their generalization capabilities is incomplete and this task is made harder by the non-convexity of the underlying learning problems.
We provide a general framework to characterize the asymptotic generalization error for single-layer neural networks (i.e., generalized linear models) with arbitrary non-linearities, making it applicable to regression as well as classification problems. This framework enables analyzing the effect of (i) over-parameterization and non-linearity during modeling; (ii) choices of loss function, initialization, and regularizer during learning; and (iii) mismatch between training and test distributions. As examples, we analyze a few special cases, namely linear regression and logistic regression. We are also able to rigorously and analytically explain the \emph{double descent} phenomenon in generalized linear models.

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