A Comparison of Two Smoothing Methods for Word Bigram Models
  A COMPARISON OF TWO SMOOTHING METHODS FOR WORD BIGRAM MODELS   Linda Bauman Peto   Department of Computer Science   University of Toronto Abstract Word bigram models estimated from text corpora require smoothing methods to estimate the probabilities of unseen bigrams. The deleted estimation method uses the formula:   Pr(i|j) = lambda f_i + (1-lambda)f_i|j, where f_i and f_i|j are the relative frequency of i and the conditional relative frequency of i given j, respectively, and lambda is an optimized parameter. MacKay (1994) proposes a Bayesian approach using Dirichlet priors, which yields a different formula:   Pr(i|j) = (alpha/F_j + alpha) m_i + (1 - alpha/F_j + alpha) f_i|j where F_j is the count of j and alpha and m_i are optimized parameters. This thesis describes an experiment in which the two methods were trained on a two-million-word corpus taken from the Canadian _Hansard_ and compared on the basis of the experimental perplexity that they assigned to a shared test corpus. The methods proved to be about equally accurate, with MacKay's method using fewer resources. 
Linda Bauman Peto (University of Toronto)