document: Improving predictions using aggregate information In domains such as consumer products or manufacturing amongst others , we have problems that warrant the prediction of a continuous target . Besides the usual set of explanatory attributes we may also have exact ( or approximate ) estimates of aggregated targets , which are the sums of disjoint sets of individual targets that we are trying to predict . Hence , the question now becomes can we use these aggregated targets , which are a coarser piece of information , to improve the quality of predictions of the individual targets ? In this paper , we provide a simple yet provable way of accomplishing this . In particular , given predictions from any regression model of the target on the test data , we elucidate a provable method for improving these predictions in terms of mean squared error , given exact ( or accurate enough ) information of the aggregated targets . These estimates of the aggregated targets may be readily available or obtained -- through multilevel regression -- at different levels of granularity . Based on the proof of our method we suggest a criterion for choosing the appropriate level . Moreover , in addition to estimates of the aggregated targets , if we have exact ( or approximate ) estimates of the mean and variance of the target distribution , then based on our general strategy we provide an optimal way of incorporating this information so as to further improve the quality of predictions of the individual targets . We then validate the results and our claims by conducting experiments on synthetic and real industrial data obtained from diverse domains .
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