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需要统计方法的发展，不损害统计准确性，但在计算上是可行的。数据质量，特别是数据测量的异质性，是影响大型数据集分析统计准确性的关键因素。该项目将探索和展示同时提高计算和统计性能的影响和可行性，以解决具有大量数据集的大数据问题。该研究将推进大数据预测统计学习的知识状态，并在与金融风险管理或商业运营相关的应用中具有极高的价值，这些应用采用推荐系统、生物学和图像分析。推动这个项目的一个关键现象是，一些精细化的集成方法与随机预测相结合，可以同时实现对大量数据的快速分析，同时提高统计性能。具体而言，该项目的目标是：(1)开发基于随机预测和随机森林的新分类方法。通过定义适当的投影，该方法可以提高具有大量不相关噪声测量的海量数据集的统计精度。将分析该方法的理论性质，并开发自适应版本的算法，以优化计算和统计效率增益；(2)提出随机投影增强算法。本文将研究随机投影增强算法的统计特性、实际性能和实现；(3)发展具有异质性的分类方法。将开发一种涉及加权自举和集成学习的分类方法，以处理大型数据集中测量的异质性或协变量移位。将随机投影方法应用于高维数据集的改进。

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.