凸空间中不适定问题的快速推理
Fast inference of ill-posed problems within a convex space
摘要：
在多种科学和技术应用中，我们面临的问题是，低维数据被证明是由一个线性模型定义在一个高维参数空间。维度的差异使得问题不明确：模型在许多参数值上与数据一致。我们的目标是找到与数据一致的参数值的概率分布，这个问题可以被看作是对高维凸多面体的探索。在这项工作中，我们引入了一种新的算法来有效地解决这个问题。它提供的结果是统计上无法区分从目前使用的数值技术，而它的运行时间与系统的大小呈线性比例。我们表明，该算法在许多抽象和实际应用中表现稳健。作为工作示例，我们模拟了限制反应通量对{ \em基因组}规模E的可行表型空间的影响。大肠杆菌代谢网络，并推断出一个真实的通信网络中的源节点和目的节点之间的流量。
英文摘要：
In multiple scientific and technological applications we face the problem of having low dimensional data to be justified by a linear model defined in a high dimensional parameter space. The difference in dimensionality makes the problem ill-defined: the model is consistent with the data for many values of its parameters. The objective is to find the probability distribution of parameter values consistent with the data, a problem that can be cast as the exploration of a high dimensional convex polytope. In this work we introduce a novel algorithm to solve this problem efficiently. It provides results that are statistically indistinguishable from currently used numerical techniques while its running time scales linearly with the system size. We show that the algorithm performs robustly in many abstract and practical applications. As working examples we simulate the effects of restricting reaction fluxes on the space of feasible phenotypes of a {\em genome} scale E. Coli metabolic network and infer the traffic flow between origin and destination nodes in a real communication network.
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。
