The problem of truth discovery arises in many areas such as database, data mining, data crowdsourcing and machine learning. It seeks trustworthy information from possibly conflicting data provided by multiple sources. Due to its practical importance, the problem has been studied extensively in recent years. Two competing models were proposed for truth discovery, weight-based model and probabilistic model. While $$(1+\epsilon )$$ ( 1 + ϵ ) -approximations have already been obtained for the weight-based model, no quality guaranteed solution has been discovered yet for the probabilistic model. In this paper, we focus on the probabilistic model and formulate it as a geometric optimization problem. Based on a sampling technique and a few other ideas, we achieve the first $$(1 + \epsilon )$$ ( 1 + ϵ ) -approximation solution. Our techniques can also be used to solve the more general multi-truth discovery problem. We validate our method by conducting experiments on both synthetic and real-world datasets (teaching evaluation data) and comparing its performance to some existing approaches. Our solutions are closer to the truth as well as global optimum based on the experimental result. The general technique we developed has the potential to be used to solve other geometric optimization problems.

中文翻译：

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逼近概率真相发现的全局最优解

真相发现问题出现在数据库、数据挖掘、数据众包和机器学习等许多领域。它从多个来源提供的可能存在冲突的数据中寻找可信赖的信息。由于其实际重要性，近年来该问题得到了广泛的研究。提出了两个相互竞争的模型用于真相发现，基于权重的模型和概率模型。虽然已经为基于权重的模型获得了 $$(1+\epsilon )$$ ( 1 + ϵ ) - 近似值，但尚未发现概率模型的质量保证解决方案。在本文中，我们关注概率模型并将其表述为几何优化问题。基于采样技术和其他一些想法，我们实现了第一个 $$(1 + \epsilon )$$ ( 1 + ϵ ) -近似解。我们的技术还可用于解决更一般的多真值发现问题。我们通过对合成数据集和真实数据集（教学评估数据）进行实验并将其性能与一些现有方法进行比较来验证我们的方法。基于实验结果，我们的解决方案更接近真实情况和全局最优解。我们开发的通用技术有可能用于解决其他几何优化问题。