The initial focus of FACTORIE was on online discriminative training with approximate gradients. Two well-known examples of this are StructuredPerceptron and ContrastiveDivergence. But often a faster and more accurate alternative is SampleRank.
Sampling in generative models can also directly perform learning, either by sampling variables that neighbor a collapsed parameter, or locally by calling estimate on certain Parameter variables.
FACTORIE also supports parameter estimation by likelihood gradient climbing with optimize.ConjugateGradient and optimize.LimitedMemoryBFGS.