Multi-D Kneser-Ney Smoothing Preserving the Original Marginal Distributions

Smoothing is an essential tool in many NLP tasks, therefore numerous techniques have been developed for this purpose in the past. One of the most widely used smoothing methods are the Kneser-Ney smoothing (KNS) and its variants, including the Modified Kneser-Ney smoothing (MKNS), which are widely considered to be among the best smoothing methods available. Although when creating the original KNS the intention of the authors was to develop such a smoothing method that preserves the marginal distributions of the original model, this property was not maintained when developing the MKNS. In this article I would like to overcome this and propose such a refined version of the MKNS that preserves these marginal distributions while keeping the advantages of both previous versions. Beside its advantageous properties, this novel smoothing method is shown to achieve about the same results as the MKNS in a standard language modelling task.