计算中的递归、概率、卷积和分类
Recursion, Probability, Convolution and Classification for Computations
摘要：
这项工作的主要动机是实用的，提供计算和理论上可扩展的方法来构建大型计算类。它开始于尝试优化R代码，用于机器学习/人工智能算法，用于巨大的数据集，由于其大小，应该以增量（在线）方式处理。我们的目标是大类的关系（基于属性），数学（基于索引）或图形计算。我们希望使用AI（人工智能）/ML（机器学习）中出现的强大计算表示，如BN（贝叶斯网络）和CNN（卷积神经网络）。对于我们所处理的计算类别，以及我们的HPC（高性能计算）需求，需要扩展将计算转换为这种表示的当前解决方案。我们的研究结果表明，我们所针对的计算类，可以是树结构的，和一个概率分布（定义一个DBN，即动态贝叶斯网络）与之相关联。更重要的是，这个DBN可以被看作是一个递归的CNN（卷积神经网络）。在该树状结构内，可以执行具有（通过可参数化的）大小界限的类中的分类。这些结果是非常强大的核心，但高度实用的算法重组和并行计算。深入介绍和揭示我们方法的全部通用性所需的数学背景）是随后论文的主题。在本文中，我们工作在一个有限的（但重要的）框架，可以理解与线性代数和图论的基础知识。重点是在适用性，本文的大部分讨论的有用性，我们的方法来解决硬编译问题的自动并行。
英文摘要：
The main motivation of this work was practical, to offer computationally and theoretical scalable ways to structuring large classes of computation. It started from attempts to optimize R code for machine learning/artificial intelligence algorithms for huge data sets, that due to their size, should be handled into an incremental (online) fashion. Our target are large classes of relational (attribute based), mathematical (index based) or graph computations. We wanted to use powerful computation representations that emerged in AI (artificial intelligence)/ML (machine learning) as BN (Bayesian networks) and CNN (convolution neural networks). For the classes of computation addressed by us, and for our HPC (high performance computing) needs, the current solutions for translating computations into such representation need to be extended. Our results show that the classes of computation targeted by us, could be tree-structured, and a probability distribution (defining a DBN, i.e. Dynamic Bayesian Network) associated with it. More ever, this DBN may be viewed as a recursive CNN (Convolution Neural Network). Within this tree-like structure, classification in classes with size bounded (by a parameterizable may be performed. These results are at the core of very powerful, yet highly practically algorithms for restructuring and parallelizing the computations. The mathematical background required for an in depth presentation and exposing the full generality of our approach) is the subject of a subsequent paper. In this paper, we work in an limited (but important) framework that could be understood with rudiments of linear algebra and graph theory. The focus is in applicability, most of this paper discuss the usefulness of our approach for solving hard compilation problems related to automatic parallelism.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
