Visual exploration of large multidimensional datasets has seen tremendous progress in recent years, allowing users to express rich data queries that produce informative visual summaries, all in real-time. The fundamental insight of these techniques is that the performance of interactive visual data exploration systems can be improved by accelerating aggregated range queries. However, the extant state techniques still have limitations, such as low expressivity and large memory footprint. In this dissertation, I present three techniques, GaussianCubes, NeuralCubes, and TopoCubes, each tackling different problems existing techniques can not solve. GaussianCubes significantly improves on datacube-based systems by providing interactive modeling capabilities, which include but are not limited to linear least squares and principal components analysis. NeuralCubes leverage the recent advancement in deep neural networks to learn a model that takes as input a given query and outputs the approximated result. The learned model serves as a real-time, low-memory approximator for aggregation queries. The model is small enough to be sent to the client side (eg the web browser for a web-based application) for evaluation, enabling subsequent exploration of large datasets without database/network connection. Finally, TopoCubes extends existing preaggregation techniques to improve the efficiency of compute-intensive tasks, such as Topological Data Analysis algorithms, again, in an interactive data analysis system.