Issues relating to the estimation of hidden Markov model (HMM) local probabilities are discussed. In particular we note the isomorphism of ra(cid:173) dial basis functions (RBF) networks to tied mixture density modellingj additionally we highlight the differences between these methods arising from the different training criteria employed. We present a method in which connectionist training can be modified to resolve these differences and discuss some preliminary experiments. Finally, we discuss some out(cid:173) standing problems with discriminative training.