  Language spreading is a complex mechanism that involves issues like culture,
economics, migration, population etc. In this paper, we propose a set of
methods to model the dynamics of the spreading system. To model the randomness
of language spreading, we propose the Batch Markov Monte Carlo Simulation with
Migration(BMMCSM) algorithm, in which each agent is treated as a language
stack. The agent learns languages and migrates based on the proposed Batch
Markov Property according to the transition matrix T and migration matrix M.
Since population plays a crucial role in language spreading, we also introduce
the Mortality and Fertility Mechanism, which controls the birth and death of
the simulated agents, into the BMMCSM algorithm. The simulation results of
BMMCSM show that the numerical and geographic distribution of languages varies
across the time. The change of distribution fits the world cultural and
economic development trend. Next, when we construct Matrix T, there are some
entries of T can be directly calculated from historical statistics while some
entries of T is unknown. Thus, the key to the success of the BMMCSM lies in the
accurate estimation of transition matrix T by estimating the unknown entries of
T under the supervision of the known entries. To achieve this, we first
construct a 20 by 20 by 5 factor tensor X to characterize each entry of T. Then
we train a Random Forest Regressor on the known entries of T and use the
trained regressor to predict the unknown entries. The reason why we choose
Random Forest(RF) is that, compared to Single Decision Tree, it conquers the
problem of over fitting and the Shapiro test also suggests that the residual of
RF subjects to the Normal distribution.
