Modern Statistical Optimization, Robustification and Inference with Applications to Big Data Analytics

现代统计优化、稳健化和推理及其在大数据分析中的应用

• 批准号: RGPIN-2018-06484
• 负责人: Sun, Qiang
• 金额: $ 1.68万
• 依托单位: University of Toronto
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2022
• 资助国家: 加拿大
• 起止时间: 2022-01-01 至 2023-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=749631
• 关键词: Modern; Statistical; Optimization; Robustification; Inference

Big data is transforming our world, revolutionizing operations and analytics everywhere, from financial engineering to biomedical sciences. How to efficiently exact useful information from large and noisy datasets is of significant importance, and it has posed at least three grand challenges. The first challenge towards this goal is often computational: the massiveness and complexity of the data call for efficient algorithms to be used in practice. The second challenge arises from the fact that the data collected in real world, big or small, are often contaminated by heavy-tailed errors or outliers, making conventional statistical methods inadequate. Third, an efficient and accurate inference procedure is in demand for big data analytics and valid statistical decision makings. We attempt to addressing these three challenges in this proposal. Our first goal of this proposal is to explore the direction of statistical optimization for nonconvex problems and to understand the hidden convexity in a wide range of continuous and discrete statistical optimization problems. We aim to provide a unified toolbox of algorithms, theories and applications, and we expect to provide new fundamental understanding and tools for optimization in big data. It, upon completed, will have potential and fundamental impact in the area of statistics, machine learning, signal processing, imaging restoration, dictionary learning and artificial intelligence. Our second goal is to comprehensively study nonasymptotic robustification for meaningful data analytics in the presence of low-quality data. The key observation is the bias-robustness tradeoff principal, which we believe is a universal phenomenon in many applications, such as prediction, classification, clustering and inference problems. This goal, upon comprehensively studied, will impact data analytics in practice. We will follow modern software principals in the emphases of compatibility, extendability and maintainability, and develop open-source packages for statisticians and practitioners. Last, we will move forward to modern statistical inference, where we focus on the replicability issues. The scientific question we aim to address is whether the discoveries from a vast statistical search can be replicated in future and independent studies. We will verify the efficacy of our methods by applying them to large-scale imaging genetic datasets, such as the enhancing neuroimaging genetics through meta-analysis and the cohorts for heart and aging research in genomic epidemiology. This goal, upon completed, will impact practitioners in various scientific disciplines, especially in neuroscience and genetics.

大数据正在改变我们的世界，彻底改变从金融工程到生物医学科学的各个领域的运营和分析。如何从大量嘈杂的数据集中有效地提取有用的信息是非常重要的，它至少提出了三个重大挑战。实现这一目标的第一个挑战通常是计算性的：数据的庞大和复杂性要求在实践中使用有效的算法。第二个挑战来自这样一个事实，即在现实世界中收集的数据，无论大小，往往受到重尾误差或异常值的污染，使得传统的统计方法不充分。第三，大数据分析和有效的统计决策需要高效、准确的推理程序。我们试图在这一建议中解决这三个挑战。我们的第一个目标是探索非凸问题的统计优化方向，并了解广泛的连续和离散统计优化问题中的隐藏凸性。我们的目标是提供一个统一的算法、理论和应用工具箱，我们期望为大数据优化提供新的基础理解和工具。一旦完成，它将在统计学、机器学习、信号处理、图像恢复、字典学习和人工智能领域产生潜在的和根本性的影响。我们的第二个目标是在存在低质量数据的情况下，全面研究有意义的数据分析的非渐近鲁棒化。关键的观察是偏差-鲁棒性权衡原则，我们认为这是许多应用中的普遍现象，例如预测，分类，聚类和推理问题。经过全面研究，这一目标将在实践中影响数据分析。我们将遵循现代软件原则，强调兼容性、可扩展性和可维护性，并为统计学家和从业人员开发开源软件包。最后，我们将继续讨论现代统计推断，重点关注可复制性问题。我们要解决的科学问题是，大规模统计研究的发现能否在未来的独立研究中得到复制。我们将通过将我们的方法应用于大规模成像遗传数据集来验证其有效性，例如通过荟萃分析增强神经成像遗传学以及基因组流行病学中心脏和衰老研究的队列。这一目标一旦完成，将影响各个科学学科的从业者，特别是神经科学和遗传学。