This paper presents the triple jump framework for accelerating the EM algorithm and other bound optimization methods. The idea is to extrapolate the third search point based on the previous two search points found by regular EM. As the convergence rate of regular EM becomes slower, the distance of the triple jump will be longer, and thus provide higher speedup for data sets where EM converges slowly. Experimental results show that the triple jump framework significantly outperforms EM and other acceleration methods of EM for a variety of probabilistic models, especially when the data set is sparse or less structured, which usually slow down EM but are common in real world data sets. The results also show that the triple jump framework is particularly effective for Cluster Models.