RI: Inference in Large-Scale Graphical Models

在这个项目中，我们将开发新的方法来实现大规模图形模型的推理，重点是从大量的传感器测量数据构建非结构化环境的模型。从大量嘈杂的传感器数据创建世界模型是一个巨大的推理问题，目前的方法不能很好地扩大规模。与最新的文献一致，我们使用图形模型对此类推理问题进行建模。然而，与文献相反，我们使用因子图而不是信任网，并表明因子图与稀疏线性代数文献之间存在密切且迄今未被充分利用的联系。这种联系使图形模型中的推理和稀疏线性代数之间能够相互促进。特别是，我们将开发一种新的图形模型范型，贝叶斯树，灵感来自稀疏线性代数的所谓多前沿分解方法中使用的表示法。就智力优势而言，这些发展是新颖的，有望显著推进机器人学和计算机视觉领域的大规模地图绘制和3D建模领域。然而，我们预计这些新的算法类别将在视觉领域的机器人之外产生广泛的影响，在每个领域都需要处理大量数据并将其浓缩在参数模型中。我们预计我们引入的新图形语言将显著提高对图形模型中精确推理的理解，因为我们觉得这在很大程度上是无法访问的，但该领域的高级研究人员。通过强调线性代数中适度的高斯消去算法与更先进的推理方法(如连接树算法)之间的联系，我们希望使新一代研究人员能够真正理解这些联系，从而能够在许多领域做出革命性的贡献。进展报告将定期更新，网址为http：//www.cc.gatech.edu/~dellaert/graph/

AbstractIn this project, we will develop novel methods to enable inference in large-scale graphical models, emphasizing the construction of models of unstructured environments from a vast number of sensor measurements. Creating models of the world from large amounts of noisy sensor data is an inference problem of vast proportions for which current methods do not scale up well. In keeping with the most recent literature, we model such inference problems using graphical models. However, in contrast to the literature we use factor graphs rather than belief nets, and show that there is a close and hithereto under-exploited connection between Factor Graphs and the sparse linear algebra literature. This connection enables cross- fertilization between inference in graphical models and sparse linear algebra. In particular, we will develop a novel graphical model paradigm, the BayesTree, inspired by the representations used in the so-called multifrontal factorization methods from sparse linear algebra.In terms of intellectual merits, these developments are novel and are expected to significantly advance the areas of large-scale mapping and 3D modeling in the fields of robotics and computer vision. However, we expect these new classes of algorithms to have broad impact beyond robotics in vision, in every fields where vast amounts of data needs to be processed and condensed in a parametric model. We expect the new graphical language we introduce to significantly improve understanding of exact inference in graphical models, as we feel this has been largely inaccessible but to advanced researchers in the field. By stressing the connections between the modest Gaussian elimination algorithm from linear algebra and more advanced inference methods such as the junction tree algorithm, we hope to enable a new generation of researchers that will truly understand these connections and hence be able to make revolutionary contributions in many fields.Progress reports will be regularly updated at http:// www.cc.gatech.edu/~dellaert/graphs/