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Maximum entropy models provide the least constrained probabilitydistributions that reproduce statistical properties of experimental datasets.In this work we characterize the learning dynamics that maximizes thelog-likelihood in the case of large but finite datasets. We first show how thesteepest descent dynamics is not optimal as it is slowed down by theinhomogeneous curvature of the model parameters space. We then provide a wayfor rectifying this space which relies only on dataset properties and does notrequire large computational efforts. We conclude by solving the long-time limitof the parameters dynamics including the randomness generated by the systematicuse of Gibbs sampling. In this stochastic framework, rather than converging toa fixed point, the dynamics reaches a stationary distribution, which for therectified dynamics reproduces the posterior distribution of the parameters.  We sum up all these insights in a "rectified" Data-Driven algorithm that isfast and by sampling from the parameters posterior avoids both under- andover-fitting along all the directions of the parameters space. Through thelearning of pairwise Ising models from the recording of a large population ofretina neurons, we show how our algorithm outperforms the steepest descentmethod.

Learning Maximum Entropy Models from finite size datasets: a fast Data-Driven algorithm allows sampling from the posterior distribution