In this paper, a novel machine learning (ML) framework is proposed for enabling a predictive, efficient deployment of unmanned aerial vehicles (UAVs), acting as aerial base stations (BSs), to provide on-demand wireless service to cellular users. In order to have a comprehensive analysis of cellular traffic, an ML framework based on a Gaussian mixture model (GMM) and a weighted expectation maximization (WEM) algorithm is introduced to predict the potential network congestion. Then, the optimal deployment of UAVs is studied to minimize the transmit power needed to satisfy the communication demand of users in the downlink, while also minimizing the power needed for UAV mobility, based on the predicted cellular traffic. To this end, first, the optimal partition of service areas of each UAV is derived, based on a fairness principle. Next, the optimal location of each UAV that minimizes the total power consumption is derived. Simulation results show that the proposed ML approach can reduce the required downlink transmit power and improve the power efficiency by over 20%, compared with an optimal deployment of UAVs with no ML prediction.