  The classical machine-learning model for support vector regression (SVR) is
widely used for regression tasks, including weather prediction, stock-market
and real-estate pricing. However, a practically realisable quantum version for
SVR remains to be formulated. We devise annealing-based algorithms, namely
simulated and quantum-classical hybrid, for training two SVR models, and
compare their empirical performances against the SVR implementation of Python's
scikit-learn package and the SVR-based state-of-the-art algorithm for the
facial landmark detection (FLD) problem. Our method is to derive a
quadratic-unconstrained-binary formulation for the optimisation problem used
for training a SVR model and solve this problem using annealing. Using D-Wave's
Hybrid Solver, we construct a quantum-assisted SVR model, thereby demonstrating
a slight advantage over classical models regarding landmark-detection accuracy.
Furthermore, we observe that annealing-based SVR models predict landmarks with
lower variances compared to the SVR models trained by greedy optimisation
procedures. Our work is a proof-of-concept example for applying quantu-assisted
SVR to a supervised learning task with a small training dataset.
