Sublinear quantum algorithms for training linear and kernel-based classifiers
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We investigate quantum algorithms for classification, a fundamental problem in machine learning, with provable guarantees. Given n d-dimensional data points, the state-of-the-art (and optimal) classical algorithm for training classifiers with constant margin runs in Õ(n+d) time. We design sublinear quantum algorithms for the same task running in Õ(√(n) +√(d)) time, a quadratic improvement in both n and d. Moreover, our algorithms use the standard quantization of the classical input and generate the same classical output, suggesting minimal overheads when used as subroutines for end-to-end applications. We also demonstrate a tight lower bound (up to poly-log factors) and discuss the possibility of implementation on near-term quantum machines. As a side result, we also give sublinear quantum algorithms for approximating the equilibria of n-dimensional matrix zero-sum games with optimal complexity Θ̃(√(n)).
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