Truth Discovery is an important learning problem arising in data analytics related fields. It concerns about finding the most trustworthy information from a dataset acquired from a number of unreliable sources. The problem has been extensively studied and a number of techniques have already been proposed. However, all of them are of heuristic nature and do not have any quality guarantee. In this paper, we formulate the problem as a high dimensional geometric optimization problem, called Entropy based Geometric Variance. Relying on a number of novel geometric techniques, we further discover new insights to this problem. We show, for the first time, that the truth discovery problem can be solved with guaranteed quality of solution. Particularly, it is possible to achieve a $(1+ϵ)$-approximation within nearly linear time under some reasonable assumptions. We expect that our algorithm will be useful for other data related applications.

真相发现是数据分析相关领域中出现的重要学习问题。它涉及从从许多不可靠来源获取的数据集中找到最可信赖的信息。已经对该问题进行了广泛的研究，并且已经提出了许多技术。但是，它们全部都是启发式的，没有任何质量保证。在本文中，我们将该问题表述为一个高维几何优化问题，称为基于熵的几何方差。依靠许多新颖的几何技术，我们进一步发现了有关此问题的新见解。我们首次表明，可以通过保证质量的解决方案来解决真相发现问题。特别是，有可能实现$（\mathrm{1个}+ϵ）$-在一些合理的假设下，近似线性时间内的近似值。我们希望我们的算法将对其他与数据相关的应用有用。