Supervised Random Feature Regression via Projection Pursuit

Jingran Zhou, Ling Zhou, shaogao lv

Keywords: Random Feature, multi-kernel, projection pursuit, semi-parametric regression, neural networks

Abstract: Random feature methods and neural network models are two popular nonparametric modeling methods, which are regarded as representatives of shallow learning and Neural Network, respectively. In practice random feature methods are short of the capacity of feature learning, while neural network methods lead to computationally heavy problems. This paper aims at proposing a flexible but computational efficient method for general nonparametric problems. Precisely, our proposed method is a feed-forward two-layer nonparametric estimation, and the first layer is used to learn a series of univariate basis functions for each projection variable, and then search for their optimal linear combination for each group of these learnt functions. Based on all the features derived in the first layer, the second layer attempts at learning a single index function with an unknown activation function. Our nonparametric estimation takes advantage of both random features and neural networks, and can be seen as an intermediate bridge between them.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Unsupervised and Self-supervised learning