As a result of decades of research and industrial development, modern query optimizers are complex software artifacts. However, the quality of the query plan chosen by an optimizer is largely determined by the quality of the underlying statistical summaries. Small selectivity estimation errors, propagated exponentially, can lead to severely sub-optimal plans. Modern optimizers typically maintain one-dimensional statistical summaries and make the attribute value independence and join uniformity assumptions for efficiently estimating selectivities. Therefore, selectivity estimation errors in today’s optimizers are frequently caused by missed correlations between attributes. We present a selectivity estimation approach that does not make the independence assumptions. By carefully using concepts from the field of graphical models, we are able to factor the joint probability distribution of all the attributes in the database into small, usually two-dimensional distributions. We describe several optimizations that can make selectivity estimation highly efficient, and we present a complete implementation inside PostgreSQL’s query optimizer. Experimental results indicate an order of magnitude better selectivity estimates, while keeping optimization time in the range of tens of milliseconds.