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 (DPP) that enhance popular techniques such as the multivariate imputation by chained equations and MissForest. Their advantages are twofold: 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 perform quantum hardware experiments by applying the quantum circuits for DPP sampling since such quantum algorithms provide a computational advantage with respect to classical ones. We demonstrate competitive results with up to 10 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 demanding high precision, such as in pharmaceutical drug trials where our approach can provide higher confidence in the predictions made.

Interacting molecules create regulatory architectures that can persist despite turnover of molecules. Although epigenetic changes occur within the context of such architectures, there is limited understanding of how they can influence the heritability of changes. Here, I develop criteria for the heritability of regulatory architectures and use quantitative simulations of interacting regulators parsed as entities, their sensors, and the sensed properties to analyze how architectures influence heritable epigenetic changes. Information contained in regulatory architectures grows rapidly with the number of interacting molecules and its transmission requires positive feedback loops. While these architectures can recover after many epigenetic perturbations, some resulting changes can become permanently heritable. Architectures that are otherwise unstable can become heritable through periodic interactions with external regulators, which suggests that mortal somatic lineages with cells that reproducibly interact with the immortal germ lineage could make a wider variety of architectures heritable. Differential inhibition of the positive feedback loops that transmit regulatory architectures across generations can explain the gene-specific differences in heritable RNA silencing observed in the nematode Caenorhabditis elegans. More broadly, these results provide a foundation for analyzing the inheritance of epigenetic changes within the context of the regulatory architectures implemented using diverse molecules in different living systems.