Quantum Sparse Support Vector Machines

Abstract

We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fraction of the input features in making decisions, and is especially useful when the total number of features, $p$, approaches or exceeds the number of training samples, $m$. We prove a $\Omega (m)$ worst-case lower bound for computational complexity of any quantum training algorithm relying on black-box access to training samples; quantum sparse SVM has at least linear worst-case complexity. However, we prove that there are realistic scenarios in which a sparse linear classifier is expected to have high accuracy, and can be trained in sublinear time in terms of both the number of training samples and the number of features.

Cited by in corpus (2)

• Quantum algorithms for Second-Order Cone Programming and Support Vector Machines
• Quantum Semi-Supervised Kernel Learning