As defined in <cite>[4]</cite> , a trans-dimensional random field model represents the joint probability of the pair (l, x l ) as where n l /n is the empirical probability of length l. f ( T is the feature vector, which is usually defined to be position-independent and length-independent, e.g. is the normalization constant of length l. By making explicit the role of length in model definition, it is clear that the model in (1) is a mixture of random fields on sentences of different lengths (namely on subspaces of different dimensions), and hence will be called a trans-dimensional random field (TRF).