The Directional Bias Helps Stochastic Gradient Descent to Generalize in Kernel Regression Models | IEEE Conference Publication | IEEE Xplore

The Directional Bias Helps Stochastic Gradient Descent to Generalize in Kernel Regression Models


Abstract:

We study the Stochastic Gradient Descent (SGD) algorithm in nonparametric statistics: kernel regression in particular. The directional bias property of SGD, which is know...Show More

Abstract:

We study the Stochastic Gradient Descent (SGD) algorithm in nonparametric statistics: kernel regression in particular. The directional bias property of SGD, which is known in the linear regression setting, is generalized to the kernel regression. More specifically, we prove that SGD with moderate and annealing step-size converges along the direction of the eigenvector that corresponds to the largest eigenvalue of the Gram matrix. In addition, the Gradient Descent (GD) with a moderate or small step-size converges along the direction that corresponds to the smallest eigenvalue. These facts are referred to as the directional bias properties; they may interpret how an SGD-computed estimator has a potentially smaller generalization error than a GD-computed estimator. The application of our theory is demonstrated by simulation studies and a case study that is based on the FashionMNIST dataset.
Date of Conference: 26 June 2022 - 01 July 2022
Date Added to IEEE Xplore: 03 August 2022
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Conference Location: Espoo, Finland
School of Industrial and Systems Engineering, Georgia Institute of Technology
School of Industrial and Systems Engineering, Georgia Institute of Technology
School of Industrial and Systems Engineering, Georgia Institute of Technology

School of Industrial and Systems Engineering, Georgia Institute of Technology
School of Industrial and Systems Engineering, Georgia Institute of Technology
School of Industrial and Systems Engineering, Georgia Institute of Technology

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