Numerical stability in data science

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Data analyses are broadly impacted by numerical errors resulting from approximations used by all computers, which questions the accuracy, robustness, and reproducibility of derived predictions. The current solutions to address this issue mask the effects of numerical errors without addressing them or do not scale to the large software ecosystems used in data science. Thus, numerical instability is an important issue that threatens the trustworthiness of data science. The long-term goal of this research program is to support the numerical reliability of data science. In the coming years, it will aim at (1) quantifying the impact of numerical variability on a wide range of data science analyses, (2) enhancing the accuracy of data science predictions by leveraging numerical variability, and (3) accelerating data science through more efficient numerical representations. To achieve these objectives, I will rely on new software technologies developed in my research group to enable systematic numerical evaluations of large codebases and accurately pinpoint numerical issues. Moreover, I will develop novel frameworks to design data analyses mindful of numerical variability, resulting in increased robustness. Finally, I will take advantage of recent CPU hardware advances to substantially accelerate analyses where high numerical precision is not required. The impact of the proposed program stems from the development of high-risk ideas over a solid base of established technologies and preliminary data. The results of this research will broadly impact data science in academia and industry by improving the accuracy, robustness, precision, and efficiency of data-driven predictions. More specifically, data scientists will have novel ways to quantify the numerical reliability of their predictions, correct them accordingly, and substantially reduce their computational requirements. Furthermore, this program will be applied specifically to neurodata science and particularly to analyses involving Magnetic Resonance Imaging data of the brain. As a result, it will directly impact Canadian health by strengthening data-driven predictions related to various neurological disorders. This research program will train a diverse group of highly qualified personnel in data science, machine learning, numerical analysis, medical image analysis, software development, and high-performance computing, all skills in high demand in the academic and industrial job markets. Through a sustained involvement in open-science initiatives, it will maximize scientific impact while ensuring equity, diversity, and inclusion.