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, 2014

"... In many applications, independence of event occurrences is assumed, even if there is evidence for dependence. Capturing dependence leads to complex models, and even if the complex models were superior, they fail to beat the simplicity and scalability of the independence assumption. Therefore, many m ..."

Abstract
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In many applications, independence of event occurrences is assumed, even if there is evidence for dependence. Capturing dependence leads to complex models, and even if the complex models were superior, they fail to beat the simplicity and scalability of the independence assumption. Therefore, many models assume independence and apply heuristics to improve results. Theoretical explanations of the heuristics are seldom given or generalizable. This paper reports that some of these heuristics can be explained as encoding dependence in an exponent based on the generalized harmonic sum. Unlike independence, where the probability of subsequent occurrences of an event is the product of the sin-gle event probability, harmony is based on a product with decaying exponent. For independence, the sequence probability is p1+1+···+1 = pn, whereas for harmony, it is p1+1/2+···+1/n. The generalized harmonic sum leads to a spectrum of harmony assumptions. This paper shows that harmony assump-tions naturally extend probability theory. An experimental evaluation for information retrieval (IR; term occurrences) and social networks (SN’s; user interactions) shows that assuming harmony is more suitable than assuming independence. The potential impact of harmony assumptions lies beyond IR and SN’s, since many applications rely on probability theory and apply heuristics to com-pensate the independence assumption. Given the concept of harmony assumptions, the dependence between multiple occurrences of an event can be reflected in an intuitive and effective way.