CAREER: Scalable Machine Learning for Astrostatistics

该奖项是根据2009年美国复苏和再投资法案(公法111-5)资助的。该项目正在设计新的数据结构和高效算法，以将现代机器学习技术扩展到海量数据集，并将其应用于最近的天空测量，以解决天文学中的核心问题。长期目标是通过专注于关键的计算原语，并通过创建允许后代做同样的教育计划来扩大所有最好的机器学习技术的规模。从短期来看，该项目正在加速奇异值分解(SVD)，这是机器学习中许多最先进的方法(以及更远的方法)中的关键计算瓶颈。除了经典的主成分分析，我们还考虑将我们的思想应用于核岭回归、图形模型推理和最大方差展开，每一种都代表一个更大的类别(核化、图形和凸模型)。与领先的天体物理学家合作，我们在一个基本的天文数据分析问题中验证了每一个问题：分别是到对象的距离估计，不同星表中对象的交叉匹配，以及发现新类型的对象。关键的洞察力是使用一种名为余弦树的新数据结构，该结构根据矢量的相互正交性对矢量进行划分，使用基于距离的几何问题的成功想法的类比来实现一种新的蒙特卡罗抽样技术。初步结果表明，在中等规模的问题中，与精确的奇异值分解相比，速度提高了20,000倍，用户可指定的高逼近精度。这项工作的更广泛影响是，利用先进的数据分析技术来挖掘当前和未来千万亿级数据集中的科学、工程和商业的潜在洞察力。与这些目标相称的是，该项目的教育目标是将真实世界的数据分析和跨学科思维深度整合到传统计算程序中。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).This project is designing new data structures and efficient algorithms for scaling modern machine learning techniques to massive datasets, and their application to recent sky surveys to solve central problems in astronomy. The long term goal is to scale up all the best machine learning techniques, by focusing on key computational primitives, and by creating the educational initiatives to allow future generations to do the same.In the shorter term, the project is accelerating the singular value decomposition (SVD), the key computational bottleneck in a number of state-of-the-art methods in machine learning (and well beyond). In addition to the classic principal component analysis, we consider the application of our ideas to kernel ridge regression, graphical model inference, and maximum variance unfolding, each representing a larger class (kernelized, graphical, and convex models). Working with leading astrophysicist collaborators, we validate each of these in a fundamental astronomical data analysis problem: respectively, estimation of the distances to objects, cross-matching of objects in different catalogs, and discovery of new types of objects. The key insight is the use of a new data structure called a cosine tree, which partitions vectors based on their mutual orthogonality, using analogies of successful ideas for distance-based geometric problems to enable a new Monte Carlo sampling technique. Preliminary results demonstrate as much as 20,000 times speedup over exact SVD in moderate-sized problems with user-specifiable high approximation accuracy.The broader impact of the work is the transformative ability to utilize the advanced data analysis techniques to unlock the potential insights across science, engineering, and business lying within the tera- and peta-scale datasets of the present and future. Apropos these goals, the project educational goals are deep integration of real-world data analysis, and cross-disciplinary thinking into traditional computing programs.