Efficient fusion of aggregated historical data

Background. In this paper, we address the challenge of recovering a time sequence of counts from aggregated historical data. For example, given a mixture of the monthly and weekly sums, how can we find the daily counts of people infected with flu? In general, what is the best way to recover historical counts from aggregated, possibly overlapping historical reports, in the presence of missing values? Equally importantly, how much should we trust this reconstruction? Current methods fail to handle complex cases such as missing value, conflicting and overlapping report, while our method not only deal with these cases successfully, but also recover the time sequence with higher accuracy by incorporating domain knowledge.