Improved clinical data imputation via classical and quantum determinantal point processes

Imputing data is a critical issue for machine learning practitioners, including in the life sciences domain, where missing clinical data is a typical situation and the reliability of the imputation is of great importance. Currently, there is no canonical approach for imputation of clinical data and widely used algorithms introduce variance in the downstream classification. Here we propose novel imputation methods based on determinantal point processes that enhance popular techniques such as the Multivariate Imputation by Chained Equations (MICE) and MissForest. Their advantages are two-fold: improving the quality of the imputed data demonstrated by increased accuracy of the downstream classification; and providing deterministic and reliable imputations that remove the variance from the classification results. We experimentally demonstrate the advantages of our methods by performing extensive imputations on synthetic and real clinical data. We also develop quantum circuits for implementing determinantal point processes, since such quantum algorithms provide a computational advantage with respect to classical ones. We demonstrate competitive results with up to ten qubits for small-scale imputation tasks on a state-of-the-art IBM quantum processor. Our classical and quantum methods improve the effectiveness and robustness of clinical data prediction modeling by providing better and more reliable data imputations. These improvements can add significant value in settings where where high precision is critical, such as in pharmaceutical drug trials where our approach can provide higher confidence in the predictions made.