Symbolic Variable Elimination for Discrete and Continuous Graphical Models
Symbolic Variable Elimination for Discrete and Continuous Graphical Models
复制标题
离散和连续图形模型的符号变量消除
DOI：
10.1609/aaai.v26i1.8406
复制
发表时间：
2012
期刊：
影响因子：
--
通讯作者：
Ehsan Abbasnejad
中科院分区：
文献类型：
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作者：
S. Sanner;Ehsan Abbasnejad
现实世界中的概率推理通常需要在连续变量图形模型中进行推理，但当联合分布为非高斯分布时，几乎没有精确的闭式推理方法。为了解决这一推理赤字，我们引入SVE-著名的变量消除算法的符号扩展，以执行精确的推理在一个表达类的混合离散和连续变量的图形模型，其条件概率函数可以很好地近似为分段组合的多项式有界支持。使用这种表示，我们表明，我们可以准确地计算所有的SVE操作，并在封闭的形式，其中至关重要的是包括定积分w.r.t.多元分段多项式函数为了帮助有效的计算和紧凑的表示，这个解决方案，我们使用扩展的代数决策图（XADD）的数据结构，支持所有SVE操作。我们提供了说明性的结果SVE的概率推理查询的启发，机器人定位和跟踪应用程序，混合各种连续分布，这是第一次提出了一个通用的封闭形式的精确解这一类离散/连续图形模型。
Probabilistic reasoning in the real-world often requires inference incontinuous variable graphical models, yet there are few methods for exact, closed-form inference when joint distributions are non-Gaussian. To address this inferential deficit, we introduce SVE -- a symbolic extension of the well-known variable elimination algorithm to perform exact inference in an expressive class of mixed discrete and continuous variable graphical models whose conditional probability functions can be well-approximated as piecewise combinations of polynomials with bounded support. Using this representation, we show that we can compute all of the SVE operations exactly and in closed-form, which crucially includes definite integration w.r.t. multivariate piecewise polynomial functions. To aid in the efficient computation and compact representation of this solution, we use an extended algebraic decision diagram (XADD) data structure that supports all SVE operations. We provide illustrative results for SVE on probabilistic inference queries inspired by robotics localization and tracking applications that mix various continuous distributions; this represents the first time a general closed-form exact solution has been proposed for this expressive class of discrete/continuous graphical models.