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This paper introduces fsLDA, a fast variational inference method for supervised LDA, which overcomes the computational limitations of the original supervised LDA and enables its application in large-scale video datasets. In addition to its scalability, our method also overcomes the drawbacks of standard, unsupervised LDA for video, including its focus on dominant but often irrelevant video information (e.g. background, camera motion). As a result, experiments in the UCF11 and UCF101 datasets show that our method consistently outperforms unsupervised LDA in every metric. Furthermore, analysis shows that class-relevant topics of fsLDA lead to sparse video representations and encapsulate high-level information corresponding to parts of video events, which we denote "micro-events".