MSPA - AST: Sparse Representation and Efficient Inference for Astronomical Spectra

最近的天文调查已经建立了数亿个物体的目录，这是十年前无法想象的数据量。 在这些数据中，高分辨率的星系光谱为阐明星系的结构和演化提供了前所未有的机会。 需要新的统计技术来充分利用这些高质量数据的诊断能力。 该项目侧重于三个相互关联的目标，每个目标都指向从光谱中提取有用信息的目标，同时对结果进行有意义的不确定性测量。 首先，研究人员研究了提取和识别星系光谱特征的有效方法，这些特征对于后续的推理任务至关重要，例如流形学习，分类和回归。 其次，研究人员创建了这些数据的非线性流形表示，反映了整个数据集合中的内在几何形状和自然变化。第三，研究人员探索天文光谱与关键物理/结构特性之间的关系。 通过前两个目标的方法实现的表示是至关重要的，因为人们需要丢弃光谱中没有信息的维度，并保留少量有物理意义的维度，以便进行有效的推断和预测。目前天体物理学数据收集的速度远远超过科学家分析数据的速度。研究人员开发的新统计工具允许对数百万个星系光谱进行快速计算分析。信息的提取是由数据的固有结构以及所问的特定问题指导的。最后，虽然研究人员专注于星系光谱，但他们的方法直接适用于其他高度复杂的数据库的分析;例如，高光谱遥感图像数据，医学研究的光谱数据和人类遗传数据。这项研究将推进统计理论，并提供广泛适用于一系列科学学科的新方法。

Recent astronomical surveys have built catalogs of hundreds of millions of objects, a volume of data that was inconceivable as recently as a decade ago. Among these data are high-resolution galaxy spectra that offer an unprecedented opportunity for elucidating the structure and evolution of galaxies. New statistical techniques are needed to harness the full diagnostic power of these high-quality data. This project focuses on three interrelated aims, each pointed towards the goal of extracting useful information from spectra, while attaching meaningful measures of uncertainty to results. First, the investigators study efficient methods for extracting and identifying features in galaxy spectra that are essential for subsequent inference tasks, such as manifold learning, classification, and regression. Second, the investigators create a non-linear manifold representation of these data that reflects the intrinsic geometry and natural variations in the entire data ensemble. Third, the investigators probe the relationship between astronomical spectra and key physical/structural properties. The representations achieved via the methods of the first two goals are crucial, as one needs to discard uninformative dimensions in spectra and keep a small number of physically meaningful ones for efficient inference and prediction.The current rate of data collection in astrophysics far outstrips the rate at which scientists can analyze the data. The new statistical tools that the investigators develop allow a rapid computational analysis of millions of galaxy spectra. The extraction of information is guided by the inherent structure of the data as well as the particular questions being asked. Finally, while the investigators focus on galaxy spectra, their methods are directly applicable to the analysis of other highly complex databases; for example, hyperspectral remote sensing image data, spectroscopy data for medical research, and human genetic data. The research will advance statistical theory and provide new methodologies broadly applicable to a range of scientific disciplines.