Dimension reduction techniques form the core of predictive analytics systems and they help us create a new feature space that is more helpful in predicting response variables. But these techniques do not necessarily guarantee a better predictive capability as most of them are unsupervised, especially in regression learning. In regression analysis literature, supervised dimension reduction techniques have not been explored much and in this work we provide a solution to this through probabilistic topic models. In this work, we have shown that the double mixture structure of Latent Dirichlet Allocation topic model helps us 1) to visualize feature patterns, and 2) to project features onto a topic simplex that is more predictive of responses, when compared to popular techniques like PCA and KernelPCA. Until now, topic models have not been explored in a supervised context of video analysis and in this work we introduce a Regularized supervised topic model (RSLDA) that models video and audio features and has outperformed supervised dimension reduction techniques like SPCA and Correlation based feature selection algorithms. All the models discussed in this work have been evaluated to predict continuous human emotions from video data.