Generalization Error of Generalized Linear Models in High Dimensions

• URL: http://arxiv.org/abs/2005.00180v1
• Date: Fri, 1 May 2020 02:17:47 GMT
• Title: Generalization Error of Generalized Linear Models in High Dimensions
• Authors: Melikasadat Emami, Mojtaba Sahraee-Ardakan, Parthe Pandit, Sundeep Rangan, Alyson K. Fletcher
• Abstract summary: We provide a framework to characterize neural networks with arbitrary non-linearities. We analyze the effect of regular logistic regression on learning. Our model also captures examples between training and distributions special cases.
• Score: 25.635225717360466
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. 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; and (ii) choices of loss function, initialization, and regularizer during learning. Our model also captures 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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