A Survey on Truth Discovery <s> Optimization based methods <s> We leverage crowd wisdom for multiple-choice question answering, and employ lightweight machine learning techniques to improve the aggregation accuracy of crowdsourced answers to these questions. In order to develop more effective aggregation methods and evaluate them empirically, we developed and deployed a crowdsourced system for playing the "Who wants to be a millionaire?" quiz show. Analyzing our data (which consist of more than 200,000 answers), we find that by just going with the most selected answer in the aggregation, we can answer over 90% of the questions correctly, but the success rate of this technique plunges to 60% for the later/harder questions in the quiz show. To improve the success rates of these later/harder questions, we investigate novel weighted aggregation schemes for aggregating the answers obtained from the crowd. By using weights optimized for reliability of participants (derived from the participants' confidence), we show that we can pull up the accuracy rate for the harder questions by 15%, and to overall 95% average accuracy. Our results provide a good case for the benefits of applying machine learning techniques for building more accurate crowdsourced question answering systems. <s> BIB001 </s> A Survey on Truth Discovery <s> Optimization based methods <s> In many real world applications, the same item may be described by multiple sources. As a consequence, conflicts among these sources are inevitable, which leads to an important task: how to identify which piece of information is trustworthy, i.e., the truth discovery task. Intuitively, if the piece of information is from a reliable source, then it is more trustworthy, and the source that provides trustworthy information is more reliable. Based on this principle, truth discovery approaches have been proposed to infer source reliability degrees and the most trustworthy information (i.e., the truth) simultaneously. However, existing approaches overlook the ubiquitous long-tail phenomenon in the tasks, i.e., most sources only provide a few claims and only a few sources make plenty of claims, which causes the source reliability estimation for small sources to be unreasonable. To tackle this challenge, we propose a confidence-aware truth discovery (CATD) method to automatically detect truths from conflicting data with long-tail phenomenon. The proposed method not only estimates source reliability, but also considers the confidence interval of the estimation, so that it can effectively reflect real source reliability for sources with various levels of participation. Experiments on four real world tasks as well as simulated multi-source long-tail datasets demonstrate that the proposed method outperforms existing state-of-the-art truth discovery approaches by successful discounting the effect of small sources. <s> BIB002 </s> A Survey on Truth Discovery <s> Optimization based methods <s> In many applications, one can obtain descriptions about the same objects or events from a variety of sources. As a result, this will inevitably lead to data or information conflicts. One important problem is to identify the true information (i.e., the truths) among conflicting sources of data. It is intuitive to trust reliable sources more when deriving the truths, but it is usually unknown which one is more reliable a priori. Moreover, each source possesses a variety of properties with different data types. An accurate estimation of source reliability has to be made by modeling multiple properties in a unified model. Existing conflict resolution work either does not conduct source reliability estimation, or models multiple properties separately. In this paper, we propose to resolve conflicts among multiple sources of heterogeneous data types. We model the problem using an optimization framework where truths and source reliability are defined as two sets of unknown variables. The objective is to minimize the overall weighted deviation between the truths and the multi-source observations where each source is weighted by its reliability. Different loss functions can be incorporated into this framework to recognize the characteristics of various data types, and efficient computation approaches are developed. Experiments on real-world weather, stock and flight data as well as simulated multi-source data demonstrate the necessity of jointly modeling different data types in the proposed framework. <s> BIB003 </s> A Survey on Truth Discovery <s> Optimization based methods <s> In the era of big data, information regarding the same objects can be collected from increasingly more sources. Unfortunately, there usually exist conflicts among the information coming from different sources. To tackle this challenge, truth discovery, i.e., to integrate multi-source noisy information by estimating the reliability of each source, has emerged as a hot topic. In many real world applications, however, the information may come sequentially, and as a consequence, the truth of objects as well as the reliability of sources may be dynamically evolving. Existing truth discovery methods, unfortunately, cannot handle such scenarios. To address this problem, we investigate the temporal relations among both object truths and source reliability, and propose an incremental truth discovery framework that can dynamically update object truths and source weights upon the arrival of new data. Theoretical analysis is provided to show that the proposed method is guaranteed to converge at a fast rate. The experiments on three real world applications and a set of synthetic data demonstrate the advantages of the proposed method over state-of-the-art truth discovery methods. <s> BIB004
In BIB001 BIB002 BIB003 BIB004 , the general principle of truth discovery is captured through the following optimization formulation: where d(·) is a distance function that measures the difference between the information provided by source s and the identified truth. For example, the distance function can be 0-1 loss function for categorical data, and L 2 -norm can be adopted for continuous data. The objective function measures the weighted distance between the provided information {v s o } and the identified truths {v * o }. By minimizing this function, the aggregated results {v * o } will be closer to the information from the sources with high weights. Meanwhile, if a source provides information that is far from the aggregated results, in order to minimize the total loss, it will be assigned a low weight. These ideas exactly follow the general principle of truth discovery. In this optimization formulation (Eq. (3)), two sets of variables, source weights {ws} and identified truths {v * o }, are involved. To derive a solution, coordinate descent  can be adopted, in which one set of variables are fixed in order to solve for the other set of variables. This leads to solutions in which the truth computation step and source weight estimation step are iteratively conducted until convergence. This is similar to the iterative methods.