Sparta：面向高维图形模型的稀疏表及其代数
sparta: Sparse Tables and their Algebra with a View Towards High Dimensional Graphical Models
摘要：
图模型是一个多变量（可能是非常高维的）概率模型，它是通过组合低维组件形成的。推断（条件概率的计算）基于利用条件独立结构的消息传递算法。在有限状态空间的离散变量的图形模型中，在高维中存在一个基本问题：一个离散分布由一个值表表示，在高维中，这样的表可能变得非常大。在推理中，这些表必须相乘，这可能导致更大的表。sparta包通过实现有效处理稀疏表的乘法和边缘化的方法来应对这一挑战。该软件包是用R编程语言编写的，可以从Comprehensive R Archive Network（CRAN）免费获得。CRAN上的配套软件包jti也是为了展示sparta与连接树算法的潜力而开发的。我们表明，jti是能够处理高度复杂的图形模型，否则是不可行的，由于缺乏计算机内存，使用斯巴达作为后端的表操作。
英文摘要：
A graphical model is a multivariate (potentially very high dimensional) probabilistic model, which is formed by combining lower dimensional components. Inference (computation of conditional probabilities) is based on message passing algorithms that utilize conditional independence structures. In graphical models for discrete variables with finite state spaces, there is a fundamental problem in high dimensions: A discrete distribution is represented by a table of values, and in high dimensions such tables can become prohibitively large. In inference, such tables must be multiplied which can lead to even larger tables. The sparta package meets this challenge by implementing methods that efficiently handles multiplication and marginalization of sparse tables. The package was written in the R programming language and is freely available from the Comprehensive R Archive Network (CRAN). The companion package jti, also on CRAN, was developed to showcase the potential of sparta in connection to the Junction Tree Algorithm. We show, that jti is able to handle highly complex graphical models which are otherwise infeasible due to lack of computer memory, using sparta as a backend for table operations.
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。
