Numerical stability in data science

数据分析广泛地受到所有计算机使用的近似值所产生的数值误差的影响，这对派生预测的准确性、稳健性和再现性提出了质疑。目前解决这一问题的解决方案掩盖了数字误差的影响，但没有解决这些问题，或者没有扩展到数据科学中使用的大型软件生态系统。因此，数值不稳定性是威胁数据科学可信度的一个重要问题。这项研究计划的长期目标是支持数据科学的数值可靠性。在未来几年，它的目标将是(1)量化数值变异性对广泛的数据科学分析的影响，(2)通过利用数值变异性来提高数据科学预测的准确性，以及(3)通过更有效的数值表示来加速数据科学。为了实现这些目标，我将依靠我的研究小组开发的新软件技术来实现对大型代码库的系统数字评估，并准确地定位数字问题。此外，我将开发新的框架来设计数据分析，同时考虑到数字的可变性，从而提高稳健性。最后，我将利用最新的CPU硬件进步，在不需要高数值精度的情况下大幅加速分析。拟议计划的影响源于在现有技术和初步数据的坚实基础上开发高风险想法。这项研究的结果将通过提高数据驱动预测的准确性、稳健性、精确度和效率，广泛影响学术界和工业界的数据科学。更具体地说，数据科学家将有新的方法来量化他们预测的数字可靠性，并相应地进行修正，并大幅减少他们的计算要求。此外，该程序将专门应用于神经数据科学，特别是涉及大脑磁共振成像数据的分析。因此，它将通过加强与各种神经疾病相关的数据驱动的预测，直接影响加拿大的健康。这一研究计划将培养一批高素质的数据科学、机器学习、数值分析、医学图像分析、软件开发和高性能计算方面的人才，这些技能在学术和工业就业市场上都有很高的需求。通过持续参与开放科学倡议，它将最大限度地发挥科学影响，同时确保公平、多样性和包容性。

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.