We focus on data fusion, i.e., the problem of unifying conflicting data from data sources into a single representation by estimating the source accuracies. We propose SLiMFast, a framework that expresses data fusion as a statistical learning problem over discriminative probabilistic models, which in many cases correspond to logistic regression. In contrast to previous approaches that use complex generative models, discriminative models make fewer distributional assumptions over data sources and allow us to obtain rigorous theoretical guarantees. Furthermore, we show how SLiMFast enables incorporating domain knowledge into data fusion, yielding accuracy improvements of up to 50% over state-of-the-art baselines. Building upon our theoretical results, we design an optimizer that obviates the need for users to manually select an algorithm for learning SLiMFast's parameters. We validate our optimizer on multiple real-world datasets and show that it can accurately predict the learning algorithm that yields the best data fusion results.