Latent OLAP: data cubes over latent variables

We introduce a novel class of data cube, called latent-variable cube. For many data analysis tasks, data in a database can be represented as points in a multi-dimensional space. Ordinary data cubes compute aggregate functions over these "observed" data points for each cell (i.e., region) in the space, where the cells have different granularities defined by hierarchies. While useful, data cubes do not provide sufficient capability for analyzing "latent variables" that are often of interest but not directly observed in data. For example, when analyzing users' interaction with online advertisements, observed data informs whether a user clicked an ad or not. However, the real interest is often in knowing the click probabilities of ads for different user populations. In this example, click probabilities are latent variables that are not observed but have to be estimated from data. We argue that latent variables are a useful construct for a number of OLAP application scenarios. To facilitate such analyses, we propose cubes that compute aggregate functions over latent variables. Specifically, we discuss the pitfalls of common practice in scenarios where latent variables should, but are not considered; we rigorously define latent-variable cube based on Bayesian hierarchical models and provide efficient algorithms. Through extensive experiments on both simulated and real data, we show that our method is accurate and runs orders of magnitude faster than the baseline.