Using continuous features in the maximum entropy model

We investigate the problem of using continuous features in the maximum entropy (MaxEnt) model. We explain why the MaxEnt model with the moment constraint (MaxEnt-MC) works well with binary features but not with the continuous features. We describe how to enhance constraints on the continuous features and show that the weights associated with the continuous features should be continuous functions instead of single values. We propose a spline-based solution to the MaxEnt model with non-linear continuous weighting functions and illustrate that the optimization problem can be converted into a standard log-linear model at a higher-dimensional space. The empirical results on two classification tasks that contain continuous features are reported. The results confirm our insight and show that our proposed solution consistently outperforms the MaxEnt-MC model and the bucketing approach with significant margins.