Signal Processing and Information Extraction, from Data to Complex Models and Structures

本研究的重点是在大规模数据存在的复杂系统和结构的统计学习。我们收集大量数据的能力不断提高，迫切需要对这些收集到的数据的底层结构进行分析、解释和建模，这是这项工作的主要动机。值得信赖的数据建模变得至关重要，特别是在使用不可靠的模型可能导致不可逆转的损害的情况下。这方面的例子包括根据各种卫生部门数据分析采取的行动和根据从大量收集的数据得出的结论作出的环境决定。 尽管我们在存储“大”数据方面具有优势，但它们也带来了适当信息提取的固有“大”挑战。在真实的应用中，数据集的基数和成员维都很大，这就要求抽取低维的信息数据。这一领域的大部分研究现在都致力于通过诸如开发有效的张量分析和/或设计自适应核函数等方法来绘制数据草图。这些数据建模方法对不可避免的降维过程非常敏感。 近年来的大规模数据建模方法利用了在参数化建模中引入隐变量的优点。例如，在这个方向上，一种流行的方法是深度学习。虽然这些方法在去除大数据集上的噪声方面非常成功，但在这些方法中，诸如标记的不确定性，过拟合和收敛到真实模型的验证等问题非常重要。此外，在大数据建模的所有研究趋势中，并发复杂性分析和鲁棒性能是各种机器学习方法（如数据聚类，分类，压缩和预测结构建模）的关键任务。 该项目的主要重点是大数据建模的这些重要挑战。它将侧重于结构数据建模，复杂性分析和建模中参数数量的最佳选择的验证方法。 随着更多的数据变得可用，建模方法可以变得更加复杂，参数数量也越来越多。然而，关键的挑战是，必须监控建模复杂性的增长速度，以确保提供更精确的建模，并且不会因过拟合而失去可靠性。本研究的预期成果为可行的数据驱动结构建模提供了理论、知识和算法。该项目的直接影响是开发高效，可靠，最重要的是可验证的结构化数据建模方法。 *****

This research focuses on statistical learning of complex systems and structures in presence of large scale data. Our increasing ability to collect massive volumes of data demands an urgent need for analysis, interpretation, and modeling of the underlying structures of these collected data which is the main motivation of this work. Trustworthy data modeling becomes vital especially in scenarios where the use of unreliable model can cause irreversible damages. Examples of such cases are actions based on various health sector data analysis and environmental decisions based on conclusions from large collected data. Despite advantages of our ability in storing the “big” data, they also come with inherent “big” challenges for proper information extraction. Huge data set size, in both cardinality and member dimension, requires extracting lower dimension informative data in real applications. Much of research in this area is now dedicated to data sketching through approaches such as development of efficient tensor analysis and/or design of adaptive kernel functions. These data modeling methods are heavily sensitive to the inevitable dimension reduction process. The recent modeling approaches for large scale data take advantages of including latent variables in the parametric modeling. For example, one popular approach in this direction is deep learning. While these methods are quite successful with noise removal on the large data sets, issues such as uncertainty in labeling, overfitting, and verification of convergence to the true model are extremely important in these approaches. In addition, in all the research trends for large data modeling, simultaneous complexity analysis and robust performance are critical tasks in various machine learning methods such as data clustering, classification, compression, and predictive structural modeling. The main concentration of this project is on these important challenges of large data modeling. It will focus on validation approaches for structural data modeling, complexity analysis, and optimum choice of number of parameters in modeling. As more data becomes available, the modeling methods have the luxury of becoming more complex with higher number of parameters. The crucial challenge, however, is that the rate of growth in modeling complexity has to be monitored such that it can guarantee providing more precise modeling and doesn't lose reliability by overfitting. The intended outcome of this research provides theory, knowledge, and algorithms for feasible data-driven structural modeling. Immediate impact of the project is in developing efficient, reliable, and most importantly verifiable methods of structural data modeling. *****