Abstract:
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Point processes over networks are becoming a popular topic in statistics and machine learning. The discrete nature of events data observed in social networks, crime data, medical records, etc., poses new challenges to statistical modeling and computation. Each discrete events data point typically consists of the time, location (node index), and marks (additional information about the events). The purpose is to recover the underlying influence networks, which capture the complex interdependence between the event observations. We consider the situation when the timing of each event is uncertain, an important aspect of such data that has been largely ignored in previous models. For instance, in medical records, the lab test results come out with imprecise timing (they are merely the time of lab results released rather than the actual precise time of patient conditions). Our work proposes a new model to tackle the timing uncertainty and present efficient learning algorithms based on optimization, utilizing the underlying low-rank structure of the network influence kernels. We demonstrate the good performance of the proposed model and algorithm using synthetic and real data.
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