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

Language Distribution Prediction based on Batch Markov Monte Carlo Simulation with Migration