Ultra-dense heterogeneous networks (Ud-HetNets) have been put forward to improve the network capacity for next-generation wireless networks. However, counter to the 5G vision, ultra-dense deployment of networks would significantly increase energy consumption and thus decrease network energy efficiency suffering from the conventional worst-case network design philosophy. This problem becomes particularly severe when Ud-HetNets meet big data because of the traditional reactive request-transmit service mode. In view of these, this article first develops a big-data-aware artificial intelligent based framework for energy-efficient operations of Ud-HetNets. Based on the framework, we then identify four promising techniques, namely big data analysis, adaptive base station operation, proactive caching, and interference-aware resource allocation, to reduce energy cost on both large and small scales. We further develop a load-aware stochastic optimization approach to show the potential of our proposed framework and techniques in energy conservation. In a nutshell, we devote to constructing green Ud-HetNets of big data with the abilities of learning and inferring by improving the flexibility of control from worst-case to adaptive design and shifting the manner of services from reactive to proactive modes.