加速统计和数据科学中的定点算法:最新评述

Bohao Tang, Nicholas C. Henderson, Ravi Varadhan
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引用次数: 1

摘要

不动点算法因其简单、保证收敛和适用于高维问题而在统计学和数据科学中很受欢迎。众所周知的例子包括期望最大化(EM)算法、最大化最小化(MM)和基于梯度的算法,如梯度下降(GD)和近端梯度下降。这些算法的一个特点是收敛速度慢。我们讨论了几种最先进的技术来加速它们的收敛。我们在六个不同的应用中演示并评估了这些技术的效率和健壮性。在加速方案中,SQUAREM表现出稳健的加速,平均加速18倍。DAAREM和重新启动的nesterov方案也一直表现出令人印象深刻的加速。因此,可以使用SQUAREM、DAAREM或restart - nesterov加速方案中的一种来加速原始不动点算法。我们描述了实现细节和软件包,以促进加速方案的应用。我们还讨论了针对给定问题选择特定加速方案的策略。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Accelerating Fixed-Point Algorithms in Statistics and Data Science: A State-of-Art Review
Fixed-point algorithms are popular in statistics and data science due to their simplicity, guaranteed convergence, and applicability to high-dimensional problems. Well-known examples include the expectation-maximization (EM) algorithm, majorization-minimization (MM), and gradient-based algorithms like gradient descent (GD) and proximal gradient descent. A characteristic weakness of these algorithms is their slow convergence. We discuss several state-of-art techniques for accelerating their convergence. We demonstrate and evaluate these techniques in terms of their efficiency and robustness in six distinct applications. Among the acceleration schemes, SQUAREM shows robust acceleration with a mean 18-fold speedup. DAAREM and restarted-Nesterov schemes also demonstrate consistently impressive accelerations. Thus, it is possible to accelerate the original fixed-point algorithm by using one of SQUAREM, DAAREM, or restarted-Nesterov acceleration schemes. We describe implementation details and software packages to facilitate the application of the acceleration schemes. We also discuss strategies for selecting a particular acceleration scheme for a given problem.
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