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: 2020
• 资助国家: 加拿大
• 起止时间: 2020-01-01 至 2021-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=714101
• 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。