Quantum-Assisted Feature Selection for Vehicle Price Prediction Modeling

Abstract: 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.