Contents 1. Introduction.................................................................................................. 2 2.TopicModelsandtheirApplications ........................................................................ 4 2.1.Anchorwordsandidentifiabilityof thetopicmodel.................................................... 5 2.2.Topic-SCORE:AspectralapproachtoestimatingthetopicmatrixA................................ 5 2.3.Theanchor-word-searchingmethodsforestimatingA................................................. 6 2.4.OtherapproachesforestimatingA: EMalgorithmandNMFapproaches ............................ 7 2.5. EstimatingthetopicweightmatrixW................................................................. 7 2.6.Theoptimal ratesforestimating(A,W)............................................................... 8 2.7. Estimatingthenumberof topicsK.................................................................... 8 2.8.Global testingassociatedwithtopicmodels............................................................ 9 2.9.ThelatentDirichlettopicmodelanditsestimation ................................................... 9 2.10.Them-gramtopicmodels.............................................................................. 9 2.11.Supervisedtopicmodels ................................................................................ 10