BIGDATA: Collaborative Research: F: IA: Statistical Learning for Big Data with Random Projections

当代数据驱动的科学和工程问题要求开发不影响统计精度的统计方法，但在计算上是可行的。在大数据集的分析中，数据质量，特别是数据测量的异质性，是影响统计精度的关键因素。本项目将探索和论证同时提高计算和统计性能对海量数据集大数据问题的影响和可行性。这项研究将提高大数据预测统计学习的知识水平，并在与金融风险管理或使用推荐系统、生物学和图像分析的商业运营相关的应用中具有极其重要的价值。推动这一项目的一个关键现象是，一些改进的集成方法与随机预测相结合，可以同时实现对海量数据的快速分析，同时提高统计性能。具体来说，该项目的目标是：(1)开发基于随机投影和随机森林的新的分类方法。通过定义适当的投影，该方法对于包含大量不相关噪声测量的海量数据集具有较高的统计精度。分析了该方法的理论性质，并开发了一种自适应版本的算法，以优化计算和统计效率；(2)提出了具有随机投影的Boost算法。将研究所提出的随机投影Boosting算法的统计特性、实际性能和实现；(3)开发具有异质性的分类方法。将开发一种分类方法，该方法涉及加权引导和集成学习，以处理大数据集中测量的异质性或协变量变化。将随机投影法应用于高维数据集，改进了该方法。

Contemporary data-driven science and engineering problems require the development of statistical methods that do not compromise statistical accuracy, yet are computationally feasible. Data quality, particularly the heterogeneity in data measurements, is a critical factor that affects statistical accuracy in the analysis of large datasets. This project will explore and demonstrate the impact and feasibility of improving computational and statistical performances simultaneously for Big Data problems with massive datasets. The research will advance the state of knowledge in predictive statistical learning with Big Data, and be extremely valuable in applications related to financial risk management or commercial operations employing recommender systems, biology, and image analysis. A key phenomenon motivating this project is the notion that some refined ensemble methods combined with random projections can simultaneously enable the fast analysis of massive data while enhancing statistical performance. Specifically, the aims of the project are: (1) Develop new classification methods based on random projections and the random forest. By defining appropriate projections, the proposed method is shown to improve statistical accuracy for massive datasets with a large number of irrelevant noisy measurements. The theoretical properties of this method will be analyzed, and an adaptive version of the algorithm developed to optimize the computational and statistical efficiency gains; (2) Propose boosting algorithms with random projections. The statistical properties, practical performance, and implementation of the proposed random projected boosting algorithms will be investigated; (3) Develop classification methods with heterogeneities. A classification method that involves the weighted bootstrap and ensemble learning to handle heterogeneity or covariate shifts in measurements in large datasets will be developed. The random projection method will be applied to improve the proposed method for high-dimensional datasets.