Web-based online interactive visual analytics enjoys popularity in recent years. Traditionally, visualizations are produced directly from querying the underlying data. However, for a very large dataset, this way is so time-consuming that it cannot meet the low-latency requirements of interactive visual analytics. In this paper, we propose a learning-based visualization approach called BlinkViz, which uses a learned model to produce approximate visualizations by leveraging mixed sum-product networks to learn the distribution of the original data. In such a way, it makes visualization faster and more scalable by decoupling visualization and data. In addition, to improve the accuracy of approximate visualizations, we propose an enhanced model by incorporating a neural network with residual structures, which can refine prediction results, especially for visual requests with low selectivity. Extensive experiments show that BlinkViz is extremely fast even on a large dataset with hundreds of millions of data records (over 30GB), responding in sub-seconds (from 2ms to less than 500ms for different requests) while keeping a low error rate. Furthermore, our approach remains scalable on latency and memory footprint size regardless of data size.