Quantum Sparse Support Vector Machines

We present a quantum machine learning algorithm for training Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector. Sparse SVM results in a classifier that uses only a small fraction of the input features in making decisions, and is especially suitable for cases where the total number of features is at the same order, or larger, than the number of training samples. The algorithm utilizes recently proposed quantum solvers for semidefinite programming and linear programming problems. We show that while for an arbitrary binary classification problem no quantum speedup is achieved by using quantum SDP/LP solvers during training, there are realistic scenarios in which using a sparse linear classifier makes sense in terms of the expected accuracy of predictions, and polynomial quantum speedup compared to classical methods can be achieved.