document: Information integration over time in unreliable and uncertain environments Often an interesting true value such as a stock price , sports score , or current temperature is only available via the observations of noisy and potentially conflicting sources . Several techniques have been proposed to reconcile these conflicts by computing a weighted consensus based on source reliabilities , but these techniques focus on static values . When the real-world entity evolves over time , the noisy sources can delay , or even miss , reporting some of the real-world updates . This temporal aspect introduces two key challenges for consensus-based approaches : ( i ) due to delays , the mapping between a source 's noisy observation and the real-world update it observes is unknown , and ( ii ) missed updates may translate to missing values for the consensus problem , even if the mapping is known . To overcome these challenges , we propose a formal approach that models the history of updates of the real-world entity as a hidden semi-Markovian process ( HSMM ) . The noisy sources are modeled as observations of the hidden state , but the mapping between a hidden state ( i.e. real-world update ) and the observation ( i.e. source value ) is unknown . We propose algorithms based on Gibbs Sampling and EM to jointly infer both the history of real-world updates as well as the unknown mapping between them and the source values . We demonstrate using experiments on real-world datasets how our history-based techniques improve upon history-agnostic consensus-based approaches .
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