Classification models may often suffer from “structure imbalance” between training and testing data that may occur due to the deficient data collection process. This imbalance can be represented by the learning using privileged information (LUPI) paradigm. In this paper, we present a supervised probabilistic classification approach that integrates LUPI into a hidden conditional random field (HCRF) model. The proposed model is called LUPI-HCRF and is able to cope with additional information that is only available during training. Moreover, the proposed method employes Student’s t-distribution to provide robustness to outliers by modeling the conditional distribution of the privileged information. Experimental results in three publicly available datasets demonstrate the effectiveness of the proposed approach and improve the state-of-the-art in the LUPI framework for recognizing human activities.