The And-Or graph is a tool for knowledge representation. In this thesis we first study thesampling of the And-Or graph with or without context constraints. Without any constrainton the potential functions of the And-Or graph nodes, the positions and shapes of differ-ent components of the face images are not aligned properly. In contrast, with both unaryconstraints and binary constraints, the components are aligned and the samples are morerepresentative of the And-Or graph. We further explore parameter and structure learning ofthe And-Or graph by implementing and applying some existing algorithms. The experimen-tal results on 1D text data and 2D face image data are shown. While there is no apparentdifference between the sampling results of the parameter learned And-Or graph and the trueAnd-Or graph, the sampling results of the structure learned And-Or graph are not perfectand could be further improved
