Big data applications such as in smart electric grids, transportation, and remote environment monitoring involve geographically dispersed sensors that periodically send back information to central nodes. In many cases, data from sensors is not available at central nodes at a frequency that is required for real-time modeling and decision-making. This may be due to physical limitations of the transmission networks, or due to consumers limiting frequent transmission of data from sensors located at their premises for security and privacy concerns. Such scenarios lead to partial data problem and raise the issue of data veracity in big data applications. We describe a novel solution to the problem of making short term predictions (up to a few hours ahead) in absence of real-time data from sensors in Smart Grid. A key implication of our work is that by using real-time data from only a small subset of influential sensors, we are able to make predictions for all sensors. We thus reduce the communication complexity involved in transmitting sensory data in Smart Grids. We use real-world electricity consumption data from smart meters to empirically demonstrate the usefulness of our method. Our dataset consists of data collected at 15-min intervals from 170 smart meters in the USC Microgrid for 7 years, totaling 41,697,600 data points.