MSplit LBI: Realizing Feature Selection and Dense Estimation Simultaneously in Few-shot and Zero-shot Learning

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Bo Zhao, Xinwei Sun, Yanwei Fu, Yuan Yao, Yizhou Wang ;
Proceedings of the 35th International Conference on Machine Learning, PMLR 80:5912-5921, 2018.

Abstract

It is one typical and general topic of learning a good embedding model to efficiently learn the representation coefficients between two spaces/subspaces. To solve this task, $L_{1}$ regularization is widely used for the pursuit of feature selection and avoiding overfitting, and yet the sparse estimation of features in $L_{1}$ regularization may cause the underfitting of training data. $L_{2}$ regularization is also frequently used, but it is a biased estimator. In this paper, we propose the idea that the features consist of three orthogonal parts, namely sparse strong signals, dense weak signals and random noise, in which both strong and weak signals contribute to the fitting of data. To facilitate such novel decomposition, MSplit LBI is for the first time proposed to realize feature selection and dense estimation simultaneously. We provide theoretical and simulational verification that our method exceeds $L_{1}$ and $L_{2}$ regularization, and extensive experimental results show that our method achieves state-of-the-art performance in the few-shot and zero-shot learning.

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