where

Mixing factors *c*_{j} are tuned on-the-fly to the previously processed part of
the document using the expectation-maximization (EM) type
algorithm.
Suppose *n* words,
,
have been processed from the
beginning.
Then, considering the likelihood function
for the
mixture LM, it is straightforward to derive incrementally adjusting formula
for *c*_{j}^{(n)};

where is estimated by

with appropriate terminating condition. Note that a posterior mode may be used instead by combining some prior function at Equation (3.7).