# Tensor machines for learning target-specific polynomial features

arXiv: https://arxiv.org/abs/1504.01697 · HTML: https://mlsanity.com/paper/1504.01697/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Apr 2015.

## Built on by (most cited first, 1 of 1)

- [(MPO)2: Multivariate Polynomial Optimization based on Matrix Product Operators](https://mlsanity.com/paper/2607.15916/) (2026)

## Abstract (arXiv)

Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are target-agnostic, typically thousands of such features are necessary to achieve acceptable accuracies. In this work, we consider the problem of learning a small number of explicit polynomial features. Our approach, named Tensor Machines, finds a parsimonious set of features by optimizing over the hypothesis class introduced by Kar and Karnick for random feature maps in a target-specific manner. Exploiting a natural connection between polynomials and tensors, we provide bounds on the generalization error of Tensor Machines. Empirically, Tensor Machines behave favorably on several real-world datasets compared to other state-of-the-art techniques for learning polynomial features, and deliver significantly more parsimonious models.