  A statistical language model assigns probability to strings of arbitrary
length. Unfortunately, it is not possible to gather reliable statistics on
strings of arbitrary length from a finite corpus. Therefore, a statistical
language model must decide that each symbol in a string depends on at most a
small, finite number of other symbols in the string. In this report we propose
a new way to model conditional independence in Markov models. The central
feature of our nonuniform Markov model is that it makes predictions of varying
lengths using contexts of varying lengths. Experiments on the Wall Street
Journal reveal that the nonuniform model performs slightly better than the
classic interpolated Markov model. This result is somewhat remarkable because
both models contain identical numbers of parameters whose values are estimated
in a similar manner. The only difference between the two models is how they
combine the statistics of longer and shorter strings.
  Keywords: nonuniform Markov model, interpolated Markov model, conditional
independence, statistical language model, discrete time series.
