DNA motif finding is one of the core problems in computational biology, for which several probabilistic and discrete approaches have been developed. Most existing methods formulate motif finding as an intractable optimization problem and rely either on expectation maximization (EM) or on local heuristic searches. Another challenge is the choice of motif model: simpler models such as the position-specific scoring matrix (PSSM) impose biologically unrealistic assumptions such as independence of the motif positions, while more involved models are harder to parametrize and learn.