  Within machine learning model evaluation regimes, feature selection is a
technique to reduce model complexity and improve model performance in regards
to generalization, model fit, and accuracy of prediction. However, the search
over the space of features to find the subset of $k$ optimal features is a
known NP-Hard problem. In this work, we study metrics for encoding the
combinatorial search as a binary quadratic model, such as Generalized Mean
Information Coefficient and Pearson Correlation Coefficient in application to
the underlying regression problem of price prediction. We investigate
trade-offs in the form of run-times and model performance, of leveraging
quantum-assisted vs. classical subroutines for the combinatorial search, using
minimum redundancy maximal relevancy as the heuristic for our approach. We
achieve accuracy scores of 0.9 (in the range of [0,1]) for finding optimal
subsets on synthetic data using a new metric that we define. We test and
cross-validate predictive models on a real-world problem of price prediction,
and show a performance improvement of mean absolute error scores for our
quantum-assisted method $(1471.02 \pm{135.6})$, vs. similar methodologies such
as recursive feature elimination $(1678.3 \pm{143.7})$. Our findings show that
by leveraging quantum-assisted routines we find solutions that increase the
quality of predictive model output while reducing the input dimensionality to
the learning algorithm on synthetic and real-world data.
