Computational Foundations of Machine Learning in the Era of Big Data

机器学习（ML）是一个开发可以通过学习和经验来改进自己的软件的领域，它在很大程度上是由历史数据的可用性，以及开发高效、可扩展的算法和支持理论的需求驱动的。相反，机器学习在科学、工程和商业领域的成功，以及技术创新，导致了对大数据收集的前所未有的增长和热情，从而重新定义了计算效率并引入了系统解决方案。例如，最近Deepmind的AlphaGo系统击败了顶尖的人类围棋选手，需要1900个cpu和280个gpu来进行计算。如何在这个庞大的分布式集群中平衡计算和通信，而不影响系统吞吐量或正确性？另一方面，开发移动应用的小型初创公司可能负担不起谷歌那样的计算能力，因此通常不得不转向原始解决方案。如何为机器学习构建一个算法框架，提供“旋钮”来调整计算负载，同时对准确性有明确的、可控的损失？因此，在大数据时代满足如此多样化的计算需求对ML领域来说是一个巨大的挑战。我们试图通过三个互补的目标来解决ML和大数据中的这种计算挑战：(1)实际问题很难，但也是结构化的。多年来，设计能够利用数据和模型中的某些结构的统计方法和计算算法的重要性已经变得明显。受我们之前在稀疏性和低秩性方面的工作的鼓舞，我们建议研究ML应用中常见的两种附加结构：单调性和多模态（张量格式），并开发从这些结构的存在中受益的高效算法。(2)数据总是充满噪声和随机波动，因此减少了在ML中获得精确甚至高精度解的需要。近似计算，如果做得适当，可以显着减少ML中的计算时间。我们开始系统地研究ML中近似计算的权衡，从“降级”计算昂贵的程序到更简单和更便宜的程序，到“最优”光滑不可微函数。将非凸性的测度附加到非凸函数上。(3)分布式计算已成为处理大数据集的常态。我们提出了有界异步协议（BAP）来更好地平衡分布式机器学习系统中的通信和计算，并继续研究在BAP和可能不太严格的凸或光滑假设下典型机器学习迭代算法的加速和收敛保证。我们的工作将进一步推进机器学习的计算理论和实践，所产生的算法和系统将成为使用机器学习方法分析大数据集的基础。

Machine learning (ML), a field that develops software that can improve itself through learning and experience, has been largely driven by the availability of historical data, and by the need to develop efficient and scalable algorithms and supporting theories. Conversely, the success of ML in science, engineering, and commerce, along with technological innovations, has led to an unprecedented growth and enthusiasm in big data collection, thereby redefining computational efficiency and inviting system solutions. For example, the recent AlphaGo system of Deepmind that beats top human Go players needed 1900 CPUs and 280 GPUs to carry out the computation. How to balance computation with communication in this vast distributed cluster, without compromising system throughput or correctness? On the other hand, a small startup developing a mobile app may not afford the same computational power as Google, hence often has to turn into primitive solutions. How to build an algorithmic framework for ML that provides ''knobs'' to adjust the computational load, with explicit, controllable loss on the accuracy? Meeting such diverse computational needs in the big data era has thus been a grand challenge for the ML field.We attempt to address such computational challenge in ML and big data, through three complementary objectives: (1) Real problems are hard, but also structured. Over the years the importance of designing statistical methodologies and computational algorithms that can exploit certain structure in data and model has become evident. Encouraged by our previous work on sparsity and low-rankness, we propose to investigate two additional structures that are common in ML applications: monotonicity and multi-modality (in the tensor format), and developing efficient algorithms that benefit from the presence of such structures. (2) Data is always noisy and full of random fluctuations, hence diminishing the need of obtaining exact or even high-precision solutions in ML. Approximate computation, if done properly, can significantly reduce the computation time in ML. We initiate a systematic study of the tradeoffs of approximate computation in ML, from ''downgrading'' computationally expensive programs to simpler and cheaper ones, to ''optimally" smooth nondifferentiable functions, and to attach measures of nonconvexity to nonconvex functions. (3) Distributed computation has become the norm in handling big datasets. We propose the Bounded Asynchronous Protocol (BAP) to better balance communication and computation in distributed ML systems, and we continue to investigate the speedups and convergence guarantees of typical ML iterative algorithms under BAP and possibly less stringent convex or smooth assumptions. Our work will further advance the computational theory and practice in ML, and the resulting algorithms and system will be fundamental for analyzing big datasets using ML methodologies.