Quantum Sparse Support Vector Machines
This work addresses computational efficiency for quantum machine learning in high-dimensional data, but it is incremental as it builds on existing quantum linear programming solvers.
The paper tackles the computational complexity of Quantum Sparse Support Vector Machines, proving a linear worst-case lower bound but identifying scenarios where sublinear training time is possible in terms of samples and features.
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 $Ω(m)$ 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.